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Best known packings of equal circles in a circle
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Numbers
$n$
normalisation 
$d_n$ or $R_n$
2
$d_n$:
2
comment: $d_2=2$. Optimality is proven by [1].
2
$R_n$:
2
comment: $R_2=2$. Optimality is proven by [1].
3
$d_n$:
1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576
comment: $d_3=\sqrt{3}$. Optimality is proven by [1].
3
$R_n$:
2.154700538379251529018297561003914911295203502540253752037204652967955344605866691387430791171499050
comment: $R_3=1+2/\sqrt{3}$. Optimality is proven by [1].
4
$d_n$:
1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
comment: $d_4=\sqrt{2}$. Optimality is proven by [1].
4
$R_n$:
2.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573
comment: $R_4=1+\sqrt{2}$. Optimality is proven by [1].
5
$d_n$:
1.175570504584946258337411909278145537195304875286291982144544961514556948324703915017008099725482672
comment: $d_5=2\sin(\pi/5)$. Optimality is proven by [1].
5
$R_n$:
2.701301616704079864363080994126022144480802807529633763673480484755768094727917933388640728557035243
comment: $R_5=1+\csc(\pi/5)$. Optimality is proven by [1].
6
$d_n$:
1
comment: $d_6=1$. Optimality is proven by [1].
6
$R_n$:
3
comment: $R_6=3$. Optimality is proven by [1].
7
$d_n$:
1
comment: $d_7=1$. Optimality is proven by [1].
7
$R_n$:
3
comment: $R_7=3$. Optimality is proven by [1].
8
$d_n$:
0.8677674782351162409515366656967175092199814555749197528890946070644065033063968430415680435489122042
comment: $d_8=2\sin(\pi/7)$. Optimality is proven by [1].
8
$R_n$:
3.304764870962486505241150223546855113444501887606321162063106296466853342778479596379111421974761794
comment: $R_8=1+\csc(\pi/7)$. Optimality is proven by [1].
9
$d_n$:
0.7653668647301795434569199680607977335226891249712540828676012712550920679201793844740275706845670943
comment: $d_9=2\sin(\pi/8)$. Optimality is proven by [1].
9
$R_n$:
3.613125929752753055713286346854374307167522376698539055097796733816162082922384101903707440385256286
comment: $R_9=1+\csc(\pi/8)$. Optimality is proven by [1].
10
$d_n$:
0.710978236
comment: Optimality is proven by [1].
10
$R_n$:
3.81302563
comment: Optimality is proven by [1].
11
$d_n$:
0.6840402866513374660881992293645191615261667350283212569300969953694295274041551991283803646770510951
comment: $d_{11}=2\sin(\pi/9)$. Optimality is proven by [2].
11
$R_n$:
3.923804400163087252232754413366291703873505661518924481710636986355345162799351809839255581031026313
comment: $R_{11}=1+\csc(\pi/9)$. Optimality is proven by [2].
12
$d_n$:
0.660152735
comment: Optimality is proven by [3].
12
$R_n$:
4.02960193
comment: Optimality is proven by [3].
13
$d_n$:
0.6180339887498948482045868343656381177203091798057628621354486227052604628189024497072072041893911375
comment: $d_{13}=(\sqrt{5}-1)/2$. Optimality is proven by [4].
13
$R_n$:
4.236067977499789696409173668731276235440618359611525724270897245410520925637804899414414408378782275
comment: $R_{13}=2+\sqrt{5}$. Optimality is proven by [4].
14
$d_n$:
0.600884161
comment: Optimality is proven by [5].
14
$R_n$:
4.32842855
comment: Optimality is proven by [5].
15
$d_n$:
0.567962868
comment: Packomania [7] lists this as the best packing known; optimality is open.
15
$R_n$:
4.52135696
comment: Packomania [7] lists this as the best packing known; optimality is open.
16
$d_n$:
0.553185219
comment: Packomania [7] lists this as the best packing known; optimality is open.
16
$R_n$:
4.61542559
comment: Packomania [7] lists this as the best packing known; optimality is open.
17
$d_n$:
0.527421466
comment: Packomania [7] lists this as the best packing known; optimality is open.
17
$R_n$:
4.79203375
comment: Packomania [7] lists this as the best packing known; optimality is open.
18
$d_n$:
0.5176380902050415246977976752480966566981378026398610276280064146301139494976039938447359493884993310
comment: Packomania [7] lists a packing with separation $2\sin(\pi/12)$ as the best known, the same separation proven optimal for $n=19$ by [6]; optimality for $n=18$ is open.
18
$R_n$:
4.863703305156273146998972798915589470535619356033618201609372305241692855919422065390246967432281808
comment: Packomania [7] lists a packing with enclosing radius $1+\csc(\pi/12)$ as the best known, the same radius proven optimal for $n=19$ by [6]; optimality for $n=18$ is open.
19
$d_n$:
0.5176380902050415246977976752480966566981378026398610276280064146301139494976039938447359493884993310
comment: $d_{19}=2\sin(\pi/12)$. Optimality is proven by [6].
19
$R_n$:
4.863703305156273146998972798915589470535619356033618201609372305241692855919422065390246967432281808
comment: $R_{19}=1+\csc(\pi/12)$. Optimality is proven by [6].
20
$d_n$:
0.485163607
comment: Packomania [7] lists this as the best packing known; optimality is open.
20
$R_n$:
5.12232074
comment: Packomania [7] lists this as the best packing known; optimality is open.
21
$d_n$:
0.470331769
comment: Packomania [7] lists this as the best packing known; optimality is open.
21
$R_n$:
5.25231748
comment: Packomania [7] lists this as the best packing known; optimality is open.
22
$d_n$:
0.450478965
comment: Packomania [7] lists this as the best packing known; optimality is open.
22
$R_n$:
5.43971896
comment: Packomania [7] lists this as the best packing known; optimality is open.
23
$d_n$:
0.440024233
comment: Packomania [7] lists this as the best packing known; optimality is open.
23
$R_n$:
5.54520422
comment: Packomania [7] lists this as the best packing known; optimality is open.
24
$d_n$:
0.429953937
comment: Packomania [7] lists this as the best packing known; optimality is open.
24
$R_n$:
5.65166109
comment: Packomania [7] lists this as the best packing known; optimality is open.
25
$d_n$:
0.420802424
comment: Packomania [7] lists this as the best packing known; optimality is open.
25
$R_n$:
5.75282433
comment: Packomania [7] lists this as the best packing known; optimality is open.
26
$d_n$:
0.414235061
comment: Packomania [7] lists this as the best packing known; optimality is open.
26
$R_n$:
5.82817654
comment: Packomania [7] lists this as the best packing known; optimality is open.
27
$d_n$:
0.407631028
comment: Packomania [7] lists this as the best packing known; optimality is open.
27
$R_n$:
5.90639785
comment: Packomania [7] lists this as the best packing known; optimality is open.
28
$d_n$:
0.398808512
comment: Packomania [7] lists this as the best packing known; optimality is open.
28
$R_n$:
6.01493810
comment: Packomania [7] lists this as the best packing known; optimality is open.
29
$d_n$:
0.389211228
comment: Packomania [7] lists this as the best packing known; optimality is open.
29
$R_n$:
6.13859790
comment: Packomania [7] lists this as the best packing known; optimality is open.
30
$d_n$:
0.384782538
comment: Packomania [7] lists this as the best packing known; optimality is open.
30
$R_n$:
6.19774107
comment: Packomania [7] lists this as the best packing known; optimality is open.
31
$d_n$:
0.377964473
comment: Packomania [7] lists this as the best packing known; optimality is open.
31
$R_n$:
6.29150262
comment: Packomania [7] lists this as the best packing known; optimality is open.
32
$d_n$:
0.368360556
comment: Packomania [7] lists this as the best packing known; optimality is open.
32
$R_n$:
6.42946297
comment: Packomania [7] lists this as the best packing known; optimality is open.
33
$d_n$:
0.364517627
comment: Packomania [7] lists this as the best packing known; optimality is open.
33
$R_n$:
6.48670312
comment: Packomania [7] lists this as the best packing known; optimality is open.
34
$d_n$:
0.356445428
comment: Packomania [7] lists this as the best packing known; optimality is open.
34
$R_n$:
6.61095709
comment: Packomania [7] lists this as the best packing known; optimality is open.
35
$d_n$:
0.351051420
comment: Packomania [7] lists this as the best packing known; optimality is open.
35
$R_n$:
6.69717109
comment: Packomania [7] lists this as the best packing known; optimality is open.
36
$d_n$:
0.348022566
comment: Packomania [7] lists this as the best packing known; optimality is open.
36
$R_n$:
6.74675379
comment: Packomania [7] lists this as the best packing known; optimality is open.
37
$d_n$:
0.347296355
comment: Packomania [7] lists this as the best packing known; optimality is open.
37
$R_n$:
6.75877048
comment: Packomania [7] lists this as the best packing known; optimality is open.
38
$d_n$:
0.335464260
comment: Packomania [7] lists this as the best packing known; optimality is open.
38
$R_n$:
6.96188697
comment: Packomania [7] lists this as the best packing known; optimality is open.
39
$d_n$:
0.330148274
comment: Packomania [7] lists this as the best packing known; optimality is open.
39
$R_n$:
7.05788416
comment: Packomania [7] lists this as the best packing known; optimality is open.
40
$d_n$:
0.326592122
comment: Packomania [7] lists this as the best packing known; optimality is open.
40
$R_n$:
7.12384644
comment: Packomania [7] lists this as the best packing known; optimality is open.
41
$d_n$:
0.319488189
comment: Packomania [7] lists this as the best packing known; optimality is open.
41
$R_n$:
7.26001233
comment: Packomania [7] lists this as the best packing known; optimality is open.
42
$d_n$:
0.315119609
comment: Packomania [7] lists this as the best packing known; optimality is open.
42
$R_n$:
7.34679641
comment: Packomania [7] lists this as the best packing known; optimality is open.
43
$d_n$:
0.311529156
comment: Packomania [7] lists this as the best packing known; optimality is open.
43
$R_n$:
7.41994486
comment: Packomania [7] lists this as the best packing known; optimality is open.
44
$d_n$:
0.307785274
comment: Packomania [7] lists this as the best packing known; optimality is open.
44
$R_n$:
7.49803668
comment: Packomania [7] lists this as the best packing known; optimality is open.
45
$d_n$:
0.304279123
comment: Packomania [7] lists this as the best packing known; optimality is open.
45
$R_n$:
7.57291233
comment: Packomania [7] lists this as the best packing known; optimality is open.
46
$d_n$:
0.300743743
comment: Packomania [7] lists this as the best packing known; optimality is open.
46
$R_n$:
7.65017991
comment: Packomania [7] lists this as the best packing known; optimality is open.
47
$d_n$:
0.297434477
comment: Packomania [7] lists this as the best packing known; optimality is open.
47
$R_n$:
7.72417005
comment: Packomania [7] lists this as the best packing known; optimality is open.
48
$d_n$:
0.294495666
comment: Packomania [7] lists this as the best packing known; optimality is open.
48
$R_n$:
7.79127143
comment: Packomania [7] lists this as the best packing known; optimality is open.
49
$d_n$:
0.290407648
comment: Packomania [7] lists this as the best packing known; optimality is open.
49
$R_n$:
7.88687096
comment: Packomania [7] lists this as the best packing known; optimality is open.
50
$d_n$:
0.287872703
comment: Packomania [7] lists this as the best packing known; optimality is open.
50
$R_n$:
7.94751527
comment: Packomania [7] lists this as the best packing known; optimality is open.
51
$d_n$:
0.284595948
comment: Packomania [7] lists this as the best packing known; optimality is open.
51
$R_n$:
8.02750695
comment: Packomania [7] lists this as the best packing known; optimality is open.
52
$d_n$:
0.282297789
comment: Packomania [7] lists this as the best packing known; optimality is open.
52
$R_n$:
8.08471719
comment: Packomania [7] lists this as the best packing known; optimality is open.
53
$d_n$:
0.278567717
comment: Packomania [7] lists this as the best packing known; optimality is open.
53
$R_n$:
8.17958283
comment: Packomania [7] lists this as the best packing known; optimality is open.
54
$d_n$:
0.277624221
comment: Packomania [7] lists this as the best packing known; optimality is open.
54
$R_n$:
8.20398238
comment: Packomania [7] lists this as the best packing known; optimality is open.
55
$d_n$:
0.277350098
comment: Packomania [7] lists this as the best packing known; optimality is open.
55
$R_n$:
8.21110255
comment: Packomania [7] lists this as the best packing known; optimality is open.
56
$d_n$:
0.270873149
comment: Packomania [7] lists this as the best packing known; optimality is open.
56
$R_n$:
8.38352992
comment: Packomania [7] lists this as the best packing known; optimality is open.
57
$d_n$:
0.268557864
comment: Packomania [7] lists this as the best packing known; optimality is open.
57
$R_n$:
8.44718465
comment: Packomania [7] lists this as the best packing known; optimality is open.
58
$d_n$:
0.265796493
comment: Packomania [7] lists this as the best packing known; optimality is open.
58
$R_n$:
8.52455377
comment: Packomania [7] lists this as the best packing known; optimality is open.
59
$d_n$:
0.263417848
comment: Packomania [7] lists this as the best packing known; optimality is open.
59
$R_n$:
8.59249996
comment: Packomania [7] lists this as the best packing known; optimality is open.
60
$d_n$:
0.261567159
comment: Packomania [7] lists this as the best packing known; optimality is open.
60
$R_n$:
8.64621985
comment: Packomania [7] lists this as the best packing known; optimality is open.
61
$d_n$:
0.261052384
comment: Packomania [7] lists this as the best packing known; optimality is open.
61
$R_n$:
8.66129758
comment: Packomania [7] lists this as the best packing known; optimality is open.
62
$d_n$:
0.255435495
comment: Packomania [7] lists this as the best packing known; optimality is open.
62
$R_n$:
8.82976541
comment: Packomania [7] lists this as the best packing known; optimality is open.
63
$d_n$:
0.253409898
comment: Packomania [7] lists this as the best packing known; optimality is open.
63
$R_n$:
8.89235154
comment: Packomania [7] lists this as the best packing known; optimality is open.
64
$d_n$:
0.251194079
comment: Packomania [7] lists this as the best packing known; optimality is open.
64
$R_n$:
8.96197111
comment: Packomania [7] lists this as the best packing known; optimality is open.
65
$d_n$:
0.249457513
comment: Packomania [7] lists this as the best packing known; optimality is open.
65
$R_n$:
9.01739732
comment: Packomania [7] lists this as the best packing known; optimality is open.
66
$d_n$:
0.247027047
comment: Packomania [7] lists this as the best packing known; optimality is open.
66
$R_n$:
9.09627943
comment: Packomania [7] lists this as the best packing known; optimality is open.
67
$d_n$:
0.244828851
comment: Packomania [7] lists this as the best packing known; optimality is open.
67
$R_n$:
9.16897188
comment: Packomania [7] lists this as the best packing known; optimality is open.
68
$d_n$:
0.243020047
comment: Packomania [7] lists this as the best packing known; optimality is open.
68
$R_n$:
9.22977375
comment: Packomania [7] lists this as the best packing known; optimality is open.
69
$d_n$:
0.241844950
comment: Packomania [7] lists this as the best packing known; optimality is open.
69
$R_n$:
9.26976127
comment: Packomania [7] lists this as the best packing known; optimality is open.
70
$d_n$:
0.239645712
comment: Packomania [7] lists this as the best packing known; optimality is open.
70
$R_n$:
9.34565319
comment: Packomania [7] lists this as the best packing known; optimality is open.
71
$d_n$:
0.237648321
comment: Packomania [7] lists this as the best packing known; optimality is open.
71
$R_n$:
9.41579690
comment: Packomania [7] lists this as the best packing known; optimality is open.
72
$d_n$:
0.236019089
comment: Packomania [7] lists this as the best packing known; optimality is open.
72
$R_n$:
9.47389086
comment: Packomania [7] lists this as the best packing known; optimality is open.
73
$d_n$:
0.234182545
comment: Packomania [7] lists this as the best packing known; optimality is open.
73
$R_n$:
9.54034615
comment: Packomania [7] lists this as the best packing known; optimality is open.
74
$d_n$:
0.232849668
comment: Packomania [7] lists this as the best packing known; optimality is open.
74
$R_n$:
9.58923276
comment: Packomania [7] lists this as the best packing known; optimality is open.
75
$d_n$:
0.230626518
comment: Packomania [7] lists this as the best packing known; optimality is open.
75
$R_n$:
9.67202963
comment: Packomania [7] lists this as the best packing known; optimality is open.
76
$d_n$:
0.229105656
comment: Packomania [7] lists this as the best packing known; optimality is open.
76
$R_n$:
9.72959680
comment: Packomania [7] lists this as the best packing known; optimality is open.
77
$d_n$:
0.227300832
comment: Packomania [7] lists this as the best packing known; optimality is open.
77
$R_n$:
9.79891192
comment: Packomania [7] lists this as the best packing known; optimality is open.
78
$d_n$:
0.225791996
comment: Packomania [7] lists this as the best packing known; optimality is open.
78
$R_n$:
9.85770990
comment: Packomania [7] lists this as the best packing known; optimality is open.
79
$d_n$:
0.224591325
comment: Packomania [7] lists this as the best packing known; optimality is open.
79
$R_n$:
9.90506347
comment: Packomania [7] lists this as the best packing known; optimality is open.
80
$d_n$:
0.223011390
comment: Packomania [7] lists this as the best packing known; optimality is open.
80
$R_n$:
9.96815181
comment: Packomania [7] lists this as the best packing known; optimality is open.
81
$d_n$:
0.221954293
comment: Packomania [7] lists this as the best packing known; optimality is open.
81
$R_n$:
10.0108642
comment: Packomania [7] lists this as the best packing known; optimality is open.
82
$d_n$:
0.220974350
comment: Packomania [7] lists this as the best packing known; optimality is open.
82
$R_n$:
10.0508242
comment: Packomania [7] lists this as the best packing known; optimality is open.
83
$d_n$:
0.219373827
comment: Packomania [7] lists this as the best packing known; optimality is open.
83
$R_n$:
10.1168579
comment: Packomania [7] lists this as the best packing known; optimality is open.
84
$d_n$:
0.218590442
comment: Packomania [7] lists this as the best packing known; optimality is open.
84
$R_n$:
10.1495309
comment: Packomania [7] lists this as the best packing known; optimality is open.
85
$d_n$:
0.218266471
comment: Packomania [7] lists this as the best packing known; optimality is open.
85
$R_n$:
10.1631115
comment: Packomania [7] lists this as the best packing known; optimality is open.
86
$d_n$:
0.215083805
comment: Packomania [7] lists this as the best packing known; optimality is open.
86
$R_n$:
10.2987011
comment: Packomania [7] lists this as the best packing known; optimality is open.
87
$d_n$:
0.213601993
comment: Packomania [7] lists this as the best packing known; optimality is open.
87
$R_n$:
10.3632085
comment: Packomania [7] lists this as the best packing known; optimality is open.
88
$d_n$:
0.212036514
comment: Packomania [7] lists this as the best packing known; optimality is open.
88
$R_n$:
10.4323377
comment: Packomania [7] lists this as the best packing known; optimality is open.
89
$d_n$:
0.210515417
comment: Packomania [7] lists this as the best packing known; optimality is open.
89
$R_n$:
10.5004918
comment: Packomania [7] lists this as the best packing known; optimality is open.
90
$d_n$:
0.209510319
comment: Packomania [7] lists this as the best packing known; optimality is open.
90
$R_n$:
10.5460692
comment: Packomania [7] lists this as the best packing known; optimality is open.
91
$d_n$:
0.209056927
comment: Packomania [7] lists this as the best packing known; optimality is open.
91
$R_n$:
10.5667722
comment: Packomania [7] lists this as the best packing known; optimality is open.
92
$d_n$:
0.206512456
comment: Packomania [7] lists this as the best packing known; optimality is open.
92
$R_n$:
10.6846458
comment: Packomania [7] lists this as the best packing known; optimality is open.
93
$d_n$:
0.205479045
comment: Packomania [7] lists this as the best packing known; optimality is open.
93
$R_n$:
10.7333526
comment: Packomania [7] lists this as the best packing known; optimality is open.
94
$d_n$:
0.204540133
comment: Packomania [7] lists this as the best packing known; optimality is open.
94
$R_n$:
10.7780322
comment: Packomania [7] lists this as the best packing known; optimality is open.
95
$d_n$:
0.203247798
comment: Packomania [7] lists this as the best packing known; optimality is open.
95
$R_n$:
10.8402050
comment: Packomania [7] lists this as the best packing known; optimality is open.
96
$d_n$:
0.202363550
comment: Packomania [7] lists this as the best packing known; optimality is open.
96
$R_n$:
10.8832028
comment: Packomania [7] lists this as the best packing known; optimality is open.
97
$d_n$:
0.201235787
comment: Packomania [7] lists this as the best packing known; optimality is open.
97
$R_n$:
10.9385901
comment: Packomania [7] lists this as the best packing known; optimality is open.
98
$d_n$:
0.200413189
comment: Packomania [7] lists this as the best packing known; optimality is open.
98
$R_n$:
10.9793831
comment: Packomania [7] lists this as the best packing known; optimality is open.
99
$d_n$:
0.199339366
comment: Packomania [7] lists this as the best packing known; optimality is open.
99
$R_n$:
11.0331412
comment: Packomania [7] lists this as the best packing known; optimality is open.
100
$d_n$:
0.198370393
comment: Packomania [7] lists this as the best packing known; optimality is open.
100
$R_n$:
11.0821497
comment: Packomania [7] lists this as the best packing known; optimality is open.
101
$d_n$:
0.197103882
comment: Packomania [7] lists this as the best packing known; optimality is open.
101
$R_n$:
11.1469336
comment: Packomania [7] lists this as the best packing known; optimality is open.
102
$d_n$:
0.196138745
comment: Packomania [7] lists this as the best packing known; optimality is open.
102
$R_n$:
11.1968635
comment: Packomania [7] lists this as the best packing known; optimality is open.
103
$d_n$:
0.194834099
comment: Packomania [7] lists this as the best packing known; optimality is open.
103
$R_n$:
11.2651436
comment: Packomania [7] lists this as the best packing known; optimality is open.
104
$d_n$:
0.193842429
comment: Packomania [7] lists this as the best packing known; optimality is open.
104
$R_n$:
11.3176586
comment: Packomania [7] lists this as the best packing known; optimality is open.
105
$d_n$:
0.193000646
comment: Packomania [7] lists this as the best packing known; optimality is open.
105
$R_n$:
11.3626596
comment: Packomania [7] lists this as the best packing known; optimality is open.
106
$d_n$:
0.191904796
comment: Packomania [7] lists this as the best packing known; optimality is open.
106
$R_n$:
11.4218344
comment: Packomania [7] lists this as the best packing known; optimality is open.
107
$d_n$:
0.190984540
comment: Packomania [7] lists this as the best packing known; optimality is open.
107
$R_n$:
11.4720518
comment: Packomania [7] lists this as the best packing known; optimality is open.
108
$d_n$:
0.190041518
comment: Packomania [7] lists this as the best packing known; optimality is open.
108
$R_n$:
11.5240161
comment: Packomania [7] lists this as the best packing known; optimality is open.
109
$d_n$:
0.189355941
comment: Packomania [7] lists this as the best packing known; optimality is open.
109
$R_n$:
11.5621191
comment: Packomania [7] lists this as the best packing known; optimality is open.
110
$d_n$:
0.188379588
comment: Packomania [7] lists this as the best packing known; optimality is open.
110
$R_n$:
11.6168616
comment: Packomania [7] lists this as the best packing known; optimality is open.
111
$d_n$:
0.187567797
comment: Packomania [7] lists this as the best packing known; optimality is open.
111
$R_n$:
11.6628112
comment: Packomania [7] lists this as the best packing known; optimality is open.
112
$d_n$:
0.186823794
comment: Packomania [7] lists this as the best packing known; optimality is open.
112
$R_n$:
11.7052745
comment: Packomania [7] lists this as the best packing known; optimality is open.
113
$d_n$:
0.186089301
comment: Packomania [7] lists this as the best packing known; optimality is open.
113
$R_n$:
11.7475281
comment: Packomania [7] lists this as the best packing known; optimality is open.
114
$d_n$:
0.185267983
comment: Packomania [7] lists this as the best packing known; optimality is open.
114
$R_n$:
11.7951734
comment: Packomania [7] lists this as the best packing known; optimality is open.
115
$d_n$:
0.184510798
comment: Packomania [7] lists this as the best packing known; optimality is open.
115
$R_n$:
11.8394740
comment: Packomania [7] lists this as the best packing known; optimality is open.
116
$d_n$:
0.183541730
comment: Packomania [7] lists this as the best packing known; optimality is open.
116
$R_n$:
11.8967045
comment: Packomania [7] lists this as the best packing known; optimality is open.
117
$d_n$:
0.182757296
comment: Packomania [7] lists this as the best packing known; optimality is open.
117
$R_n$:
11.9434755
comment: Packomania [7] lists this as the best packing known; optimality is open.
118
$d_n$:
0.182057322
comment: Packomania [7] lists this as the best packing known; optimality is open.
118
$R_n$:
11.9855510
comment: Packomania [7] lists this as the best packing known; optimality is open.
119
$d_n$:
0.181121122
comment: Packomania [7] lists this as the best packing known; optimality is open.
119
$R_n$:
12.0423344
comment: Packomania [7] lists this as the best packing known; optimality is open.
120
$d_n$:
0.180420538
comment: Packomania [7] lists this as the best packing known; optimality is open.
120
$R_n$:
12.0852125
comment: Packomania [7] lists this as the best packing known; optimality is open.
121
$d_n$:
0.179778463
comment: Packomania [7] lists this as the best packing known; optimality is open.
121
$R_n$:
12.1248031
comment: Packomania [7] lists this as the best packing known; optimality is open.
122
$d_n$:
0.178501704
comment: Packomania [7] lists this as the best packing known; optimality is open.
122
$R_n$:
12.2043748
comment: Packomania [7] lists this as the best packing known; optimality is open.
123
$d_n$:
0.177361571
comment: Packomania [7] lists this as the best packing known; optimality is open.
123
$R_n$:
12.2763999
comment: Packomania [7] lists this as the best packing known; optimality is open.
124
$d_n$:
0.176651786
comment: Packomania [7] lists this as the best packing known; optimality is open.
124
$R_n$:
12.3217083
comment: Packomania [7] lists this as the best packing known; optimality is open.
125
$d_n$:
0.175928955
comment: Packomania [7] lists this as the best packing known; optimality is open.
125
$R_n$:
12.3682253
comment: Packomania [7] lists this as the best packing known; optimality is open.
126
$d_n$:
0.175175152
comment: Packomania [7] lists this as the best packing known; optimality is open.
126
$R_n$:
12.4171444
comment: Packomania [7] lists this as the best packing known; optimality is open.
127
$d_n$:
0.174496476
comment: Packomania [7] lists this as the best packing known; optimality is open.
127
$R_n$:
12.4615495
comment: Packomania [7] lists this as the best packing known; optimality is open.
128
$d_n$:
0.173879444
comment: Packomania [7] lists this as the best packing known; optimality is open.
128
$R_n$:
12.5022222
comment: Packomania [7] lists this as the best packing known; optimality is open.
129
$d_n$:
0.173104453
comment: Packomania [7] lists this as the best packing known; optimality is open.
129
$R_n$:
12.5537178
comment: Packomania [7] lists this as the best packing known; optimality is open.
130
$d_n$:
0.172408740
comment: Packomania [7] lists this as the best packing known; optimality is open.
130
$R_n$:
12.6003400
comment: Packomania [7] lists this as the best packing known; optimality is open.
131
$d_n$:
0.171679413
comment: Packomania [7] lists this as the best packing known; optimality is open.
131
$R_n$:
12.6496205
comment: Packomania [7] lists this as the best packing known; optimality is open.
132
$d_n$:
0.171123920
comment: Packomania [7] lists this as the best packing known; optimality is open.
132
$R_n$:
12.6874368
comment: Packomania [7] lists this as the best packing known; optimality is open.
133
$d_n$:
0.170426371
comment: Packomania [7] lists this as the best packing known; optimality is open.
133
$R_n$:
12.7352731
comment: Packomania [7] lists this as the best packing known; optimality is open.
134
$d_n$:
0.169902658
comment: Packomania [7] lists this as the best packing known; optimality is open.
134
$R_n$:
12.7714462
comment: Packomania [7] lists this as the best packing known; optimality is open.
135
$d_n$:
0.169287021
comment: Packomania [7] lists this as the best packing known; optimality is open.
135
$R_n$:
12.8142548
comment: Packomania [7] lists this as the best packing known; optimality is open.
136
$d_n$:
0.168552210
comment: Packomania [7] lists this as the best packing known; optimality is open.
136
$R_n$:
12.8657596
comment: Packomania [7] lists this as the best packing known; optimality is open.
137
$d_n$:
0.167863112
comment: Packomania [7] lists this as the best packing known; optimality is open.
137
$R_n$:
12.9144699
comment: Packomania [7] lists this as the best packing known; optimality is open.
138
$d_n$:
0.167205845
comment: Packomania [7] lists this as the best packing known; optimality is open.
138
$R_n$:
12.9613043
comment: Packomania [7] lists this as the best packing known; optimality is open.
139
$d_n$:
0.166541937
comment: Packomania [7] lists this as the best packing known; optimality is open.
139
$R_n$:
13.0089872
comment: Packomania [7] lists this as the best packing known; optimality is open.
140
$d_n$:
0.165840539
comment: Packomania [7] lists this as the best packing known; optimality is open.
140
$R_n$:
13.0597775
comment: Packomania [7] lists this as the best packing known; optimality is open.
141
$d_n$:
0.165190206
comment: Packomania [7] lists this as the best packing known; optimality is open.
141
$R_n$:
13.1072553
comment: Packomania [7] lists this as the best packing known; optimality is open.
142
$d_n$:
0.164657683
comment: Packomania [7] lists this as the best packing known; optimality is open.
142
$R_n$:
13.1464116
comment: Packomania [7] lists this as the best packing known; optimality is open.
143
$d_n$:
0.163969359
comment: Packomania [7] lists this as the best packing known; optimality is open.
143
$R_n$:
13.1974008
comment: Packomania [7] lists this as the best packing known; optimality is open.
144
$d_n$:
0.163294776
comment: Packomania [7] lists this as the best packing known; optimality is open.
144
$R_n$:
13.2477892
comment: Packomania [7] lists this as the best packing known; optimality is open.
145
$d_n$:
0.162910645
comment: Packomania [7] lists this as the best packing known; optimality is open.
145
$R_n$:
13.2766686
comment: Packomania [7] lists this as the best packing known; optimality is open.
146
$d_n$:
0.162189773
comment: Packomania [7] lists this as the best packing known; optimality is open.
146
$R_n$:
13.3312338
comment: Packomania [7] lists this as the best packing known; optimality is open.
147
$d_n$:
0.161850109
comment: Packomania [7] lists this as the best packing known; optimality is open.
147
$R_n$:
13.3571125
comment: Packomania [7] lists this as the best packing known; optimality is open.
148
$d_n$:
0.161460385
comment: Packomania [7] lists this as the best packing known; optimality is open.
148
$R_n$:
13.3869394
comment: Packomania [7] lists this as the best packing known; optimality is open.
149
$d_n$:
0.160829255
comment: Packomania [7] lists this as the best packing known; optimality is open.
149
$R_n$:
13.4355485
comment: Packomania [7] lists this as the best packing known; optimality is open.
150
$d_n$:
0.160503256
comment: Packomania [7] lists this as the best packing known; optimality is open.
150
$R_n$:
13.4608064
comment: Packomania [7] lists this as the best packing known; optimality is open.
151
$d_n$:
0.160305330
comment: Packomania [7] lists this as the best packing known; optimality is open.
151
$R_n$:
13.4761915
comment: Packomania [7] lists this as the best packing known; optimality is open.
152
$d_n$:
0.159594649
comment: Packomania [7] lists this as the best packing known; optimality is open.
152
$R_n$:
13.5317485
comment: Packomania [7] lists this as the best packing known; optimality is open.
153
$d_n$:
0.158836848
comment: Packomania [7] lists this as the best packing known; optimality is open.
153
$R_n$:
13.5915367
comment: Packomania [7] lists this as the best packing known; optimality is open.
154
$d_n$:
0.158266693
comment: Packomania [7] lists this as the best packing known; optimality is open.
154
$R_n$:
13.6368977
comment: Packomania [7] lists this as the best packing known; optimality is open.
155
$d_n$:
0.157807005
comment: Packomania [7] lists this as the best packing known; optimality is open.
155
$R_n$:
13.6737086
comment: Packomania [7] lists this as the best packing known; optimality is open.
156
$d_n$:
0.157277677
comment: Packomania [7] lists this as the best packing known; optimality is open.
156
$R_n$:
13.7163628
comment: Packomania [7] lists this as the best packing known; optimality is open.
157
$d_n$:
0.156580386
comment: Packomania [7] lists this as the best packing known; optimality is open.
157
$R_n$:
13.7729919
comment: Packomania [7] lists this as the best packing known; optimality is open.
158
$d_n$:
0.155966994
comment: Packomania [7] lists this as the best packing known; optimality is open.
158
$R_n$:
13.8232259
comment: Packomania [7] lists this as the best packing known; optimality is open.
159
$d_n$:
0.155470300
comment: Packomania [7] lists this as the best packing known; optimality is open.
159
$R_n$:
13.8641934
comment: Packomania [7] lists this as the best packing known; optimality is open.
160
$d_n$:
0.154802992
comment: Packomania [7] lists this as the best packing known; optimality is open.
160
$R_n$:
13.9196469
comment: Packomania [7] lists this as the best packing known; optimality is open.
161
$d_n$:
0.154209135
comment: Packomania [7] lists this as the best packing known; optimality is open.
161
$R_n$:
13.9694003
comment: Packomania [7] lists this as the best packing known; optimality is open.
162
$d_n$:
0.153725865
comment: Packomania [7] lists this as the best packing known; optimality is open.
162
$R_n$:
14.0101723
comment: Packomania [7] lists this as the best packing known; optimality is open.
163
$d_n$:
0.153078363
comment: Packomania [7] lists this as the best packing known; optimality is open.
163
$R_n$:
14.0652037
comment: Packomania [7] lists this as the best packing known; optimality is open.
164
$d_n$:
0.152559940
comment: Packomania [7] lists this as the best packing known; optimality is open.
164
$R_n$:
14.1096014
comment: Packomania [7] lists this as the best packing known; optimality is open.
165
$d_n$:
0.152156754
comment: Packomania [7] lists this as the best packing known; optimality is open.
165
$R_n$:
14.1443393
comment: Packomania [7] lists this as the best packing known; optimality is open.
166
$d_n$:
0.151679719
comment: Packomania [7] lists this as the best packing known; optimality is open.
166
$R_n$:
14.1856784
comment: Packomania [7] lists this as the best packing known; optimality is open.
167
$d_n$:
0.151296842
comment: Packomania [7] lists this as the best packing known; optimality is open.
167
$R_n$:
14.2190466
comment: Packomania [7] lists this as the best packing known; optimality is open.
168
$d_n$:
0.150855650
comment: Packomania [7] lists this as the best packing known; optimality is open.
168
$R_n$:
14.2577069
comment: Packomania [7] lists this as the best packing known; optimality is open.
169
$d_n$:
0.150428440
comment: Packomania [7] lists this as the best packing known; optimality is open.
169
$R_n$:
14.2953582
comment: Packomania [7] lists this as the best packing known; optimality is open.
170
$d_n$:
0.150024563
comment: Packomania [7] lists this as the best packing known; optimality is open.
170
$R_n$:
14.3311503
comment: Packomania [7] lists this as the best packing known; optimality is open.
171
$d_n$:
0.149614800
comment: Packomania [7] lists this as the best packing known; optimality is open.
171
$R_n$:
14.3676614
comment: Packomania [7] lists this as the best packing known; optimality is open.
172
$d_n$:
0.149067107
comment: Packomania [7] lists this as the best packing known; optimality is open.
172
$R_n$:
14.4167761
comment: Packomania [7] lists this as the best packing known; optimality is open.
173
$d_n$:
0.148684056
comment: Packomania [7] lists this as the best packing known; optimality is open.
173
$R_n$:
14.4513414
comment: Packomania [7] lists this as the best packing known; optimality is open.
174
$d_n$:
0.148226666
comment: Packomania [7] lists this as the best packing known; optimality is open.
174
$R_n$:
14.4928488
comment: Packomania [7] lists this as the best packing known; optimality is open.
175
$d_n$:
0.147749482
comment: Packomania [7] lists this as the best packing known; optimality is open.
175
$R_n$:
14.5364265
comment: Packomania [7] lists this as the best packing known; optimality is open.
176
$d_n$:
0.147339031
comment: Packomania [7] lists this as the best packing known; optimality is open.
176
$R_n$:
14.5741357
comment: Packomania [7] lists this as the best packing known; optimality is open.
177
$d_n$:
0.146902001
comment: Packomania [7] lists this as the best packing known; optimality is open.
177
$R_n$:
14.6145184
comment: Packomania [7] lists this as the best packing known; optimality is open.
178
$d_n$:
0.146456547
comment: Packomania [7] lists this as the best packing known; optimality is open.
178
$R_n$:
14.6559276
comment: Packomania [7] lists this as the best packing known; optimality is open.
179
$d_n$:
0.145986987
comment: Packomania [7] lists this as the best packing known; optimality is open.
179
$R_n$:
14.6998513
comment: Packomania [7] lists this as the best packing known; optimality is open.
180
$d_n$:
0.145570633
comment: Packomania [7] lists this as the best packing known; optimality is open.
180
$R_n$:
14.7390349
comment: Packomania [7] lists this as the best packing known; optimality is open.
181
$d_n$:
0.145129143
comment: Packomania [7] lists this as the best packing known; optimality is open.
181
$R_n$:
14.7808297
comment: Packomania [7] lists this as the best packing known; optimality is open.
182
$d_n$:
0.144728999
comment: Packomania [7] lists this as the best packing known; optimality is open.
182
$R_n$:
14.8189306
comment: Packomania [7] lists this as the best packing known; optimality is open.
183
$d_n$:
0.144241128
comment: Packomania [7] lists this as the best packing known; optimality is open.
183
$R_n$:
14.8656708
comment: Packomania [7] lists this as the best packing known; optimality is open.
184
$d_n$:
0.143828827
comment: Packomania [7] lists this as the best packing known; optimality is open.
184
$R_n$:
14.9054183
comment: Packomania [7] lists this as the best packing known; optimality is open.
185
$d_n$:
0.143491119
comment: Packomania [7] lists this as the best packing known; optimality is open.
185
$R_n$:
14.9381448
comment: Packomania [7] lists this as the best packing known; optimality is open.
186
$d_n$:
0.143254308
comment: Packomania [7] lists this as the best packing known; optimality is open.
186
$R_n$:
14.9611857
comment: Packomania [7] lists this as the best packing known; optimality is open.
187
$d_n$:
0.142968385
comment: Packomania [7] lists this as the best packing known; optimality is open.
187
$R_n$:
14.9891068
comment: Packomania [7] lists this as the best packing known; optimality is open.
188
$d_n$:
0.142564370
comment: Packomania [7] lists this as the best packing known; optimality is open.
188
$R_n$:
15.0287507
comment: Packomania [7] lists this as the best packing known; optimality is open.
189
$d_n$:
0.142155510
comment: Packomania [7] lists this as the best packing known; optimality is open.
189
$R_n$:
15.0690994
comment: Packomania [7] lists this as the best packing known; optimality is open.
190
$d_n$:
0.141807750
comment: Packomania [7] lists this as the best packing known; optimality is open.
190
$R_n$:
15.1036015
comment: Packomania [7] lists this as the best packing known; optimality is open.
191
$d_n$:
0.141419137
comment: Packomania [7] lists this as the best packing known; optimality is open.
191
$R_n$:
15.1423575
comment: Packomania [7] lists this as the best packing known; optimality is open.
192
$d_n$:
0.141148886
comment: Packomania [7] lists this as the best packing known; optimality is open.
192
$R_n$:
15.1694352
comment: Packomania [7] lists this as the best packing known; optimality is open.
193
$d_n$:
0.140851275
comment: Packomania [7] lists this as the best packing known; optimality is open.
193
$R_n$:
15.1993745
comment: Packomania [7] lists this as the best packing known; optimality is open.
194
$d_n$:
0.140435349
comment: Packomania [7] lists this as the best packing known; optimality is open.
194
$R_n$:
15.2414287
comment: Packomania [7] lists this as the best packing known; optimality is open.
195
$d_n$:
0.139985714
comment: Packomania [7] lists this as the best packing known; optimality is open.
195
$R_n$:
15.2871722
comment: Packomania [7] lists this as the best packing known; optimality is open.
196
$d_n$:
0.139635551
comment: Packomania [7] lists this as the best packing known; optimality is open.
196
$R_n$:
15.3230000
comment: Packomania [7] lists this as the best packing known; optimality is open.
197
$d_n$:
0.139204248
comment: Packomania [7] lists this as the best packing known; optimality is open.
197
$R_n$:
15.3673777
comment: Packomania [7] lists this as the best packing known; optimality is open.
198
$d_n$:
0.138986341
comment: Packomania [7] lists this as the best packing known; optimality is open.
198
$R_n$:
15.3899032
comment: Packomania [7] lists this as the best packing known; optimality is open.
199
$d_n$:
0.138867090
comment: Packomania [7] lists this as the best packing known; optimality is open.
199
$R_n$:
15.4022604
comment: Packomania [7] lists this as the best packing known; optimality is open.
200
$d_n$:
0.138281269
comment: Packomania [7] lists this as the best packing known; optimality is open.
200
$R_n$:
15.4632749
comment: Packomania [7] lists this as the best packing known; optimality is open.
201
$d_n$:
0.137738910
comment: Packomania [7] lists this as the best packing known; optimality is open.
201
$R_n$:
15.5202253
comment: Packomania [7] lists this as the best packing known; optimality is open.
202
$d_n$:
0.137286933
comment: Packomania [7] lists this as the best packing known; optimality is open.
202
$R_n$:
15.5680288
comment: Packomania [7] lists this as the best packing known; optimality is open.
203
$d_n$:
0.136880964
comment: Packomania [7] lists this as the best packing known; optimality is open.
203
$R_n$:
15.6112355
comment: Packomania [7] lists this as the best packing known; optimality is open.
204
$d_n$:
0.136588846
comment: Packomania [7] lists this as the best packing known; optimality is open.
204
$R_n$:
15.6424841
comment: Packomania [7] lists this as the best packing known; optimality is open.
205
$d_n$:
0.136137880
comment: Packomania [7] lists this as the best packing known; optimality is open.
205
$R_n$:
15.6909883
comment: Packomania [7] lists this as the best packing known; optimality is open.
206
$d_n$:
0.135735328
comment: Packomania [7] lists this as the best packing known; optimality is open.
206
$R_n$:
15.7345575
comment: Packomania [7] lists this as the best packing known; optimality is open.
207
$d_n$:
0.135407867
comment: Packomania [7] lists this as the best packing known; optimality is open.
207
$R_n$:
15.7701906
comment: Packomania [7] lists this as the best packing known; optimality is open.
208
$d_n$:
0.135027805
comment: Packomania [7] lists this as the best packing known; optimality is open.
208
$R_n$:
15.8117641
comment: Packomania [7] lists this as the best packing known; optimality is open.
209
$d_n$:
0.134772058
comment: Packomania [7] lists this as the best packing known; optimality is open.
209
$R_n$:
15.8398714
comment: Packomania [7] lists this as the best packing known; optimality is open.
210
$d_n$:
0.134419628
comment: Packomania [7] lists this as the best packing known; optimality is open.
210
$R_n$:
15.8787794
comment: Packomania [7] lists this as the best packing known; optimality is open.
211
$d_n$:
0.134205558
comment: Packomania [7] lists this as the best packing known; optimality is open.
211
$R_n$:
15.9025125
comment: Packomania [7] lists this as the best packing known; optimality is open.
212
$d_n$:
0.133910316
comment: Packomania [7] lists this as the best packing known; optimality is open.
212
$R_n$:
15.9353691
comment: Packomania [7] lists this as the best packing known; optimality is open.
213
$d_n$:
0.133601820
comment: Packomania [7] lists this as the best packing known; optimality is open.
213
$R_n$:
15.9698559
comment: Packomania [7] lists this as the best packing known; optimality is open.
214
$d_n$:
0.133173562
comment: Packomania [7] lists this as the best packing known; optimality is open.
214
$R_n$:
16.0179958
comment: Packomania [7] lists this as the best packing known; optimality is open.
215
$d_n$:
0.132907036
comment: Packomania [7] lists this as the best packing known; optimality is open.
215
$R_n$:
16.0481123
comment: Packomania [7] lists this as the best packing known; optimality is open.
216
$d_n$:
0.132580677
comment: Packomania [7] lists this as the best packing known; optimality is open.
216
$R_n$:
16.0851545
comment: Packomania [7] lists this as the best packing known; optimality is open.
217
$d_n$:
0.132304067
comment: Packomania [7] lists this as the best packing known; optimality is open.
217
$R_n$:
16.1166933
comment: Packomania [7] lists this as the best packing known; optimality is open.
218
$d_n$:
0.132017097
comment: Packomania [7] lists this as the best packing known; optimality is open.
218
$R_n$:
16.1495529
comment: Packomania [7] lists this as the best packing known; optimality is open.
219
$d_n$:
0.131846500
comment: Packomania [7] lists this as the best packing known; optimality is open.
219
$R_n$:
16.1691551
comment: Packomania [7] lists this as the best packing known; optimality is open.
220
$d_n$:
0.131370700
comment: Packomania [7] lists this as the best packing known; optimality is open.
220
$R_n$:
16.2240948
comment: Packomania [7] lists this as the best packing known; optimality is open.
221
$d_n$:
0.131071611
comment: Packomania [7] lists this as the best packing known; optimality is open.
221
$R_n$:
16.2588343
comment: Packomania [7] lists this as the best packing known; optimality is open.
222
$d_n$:
0.130730149
comment: Packomania [7] lists this as the best packing known; optimality is open.
222
$R_n$:
16.2986898
comment: Packomania [7] lists this as the best packing known; optimality is open.
223
$d_n$:
0.130402183
comment: Packomania [7] lists this as the best packing known; optimality is open.
223
$R_n$:
16.3371666
comment: Packomania [7] lists this as the best packing known; optimality is open.
224
$d_n$:
0.130134357
comment: Packomania [7] lists this as the best packing known; optimality is open.
224
$R_n$:
16.3687316
comment: Packomania [7] lists this as the best packing known; optimality is open.
225
$d_n$:
0.129839746
comment: Packomania [7] lists this as the best packing known; optimality is open.
225
$R_n$:
16.4036038
comment: Packomania [7] lists this as the best packing known; optimality is open.
226
$d_n$:
0.129463927
comment: Packomania [7] lists this as the best packing known; optimality is open.
226
$R_n$:
16.4483187
comment: Packomania [7] lists this as the best packing known; optimality is open.
227
$d_n$:
0.129129147
comment: Packomania [7] lists this as the best packing known; optimality is open.
227
$R_n$:
16.4883699
comment: Packomania [7] lists this as the best packing known; optimality is open.
228
$d_n$:
0.128824493
comment: Packomania [7] lists this as the best packing known; optimality is open.
228
$R_n$:
16.5249981
comment: Packomania [7] lists this as the best packing known; optimality is open.
229
$d_n$:
0.128512697
comment: Packomania [7] lists this as the best packing known; optimality is open.
229
$R_n$:
16.5626646
comment: Packomania [7] lists this as the best packing known; optimality is open.
230
$d_n$:
0.128276566
comment: Packomania [7] lists this as the best packing known; optimality is open.
230
$R_n$:
16.5913123
comment: Packomania [7] lists this as the best packing known; optimality is open.
231
$d_n$:
0.127967764
comment: Packomania [7] lists this as the best packing known; optimality is open.
231
$R_n$:
16.6289361
comment: Packomania [7] lists this as the best packing known; optimality is open.
232
$d_n$:
0.127675564
comment: Packomania [7] lists this as the best packing known; optimality is open.
232
$R_n$:
16.6647046
comment: Packomania [7] lists this as the best packing known; optimality is open.
233
$d_n$:
0.127450555
comment: Packomania [7] lists this as the best packing known; optimality is open.
233
$R_n$:
16.6923600
comment: Packomania [7] lists this as the best packing known; optimality is open.
234
$d_n$:
0.127337147
comment: Packomania [7] lists this as the best packing known; optimality is open.
234
$R_n$:
16.7063359
comment: Packomania [7] lists this as the best packing known; optimality is open.
235
$d_n$:
0.127286578
comment: Packomania [7] lists this as the best packing known; optimality is open.
235
$R_n$:
16.7125758
comment: Packomania [7] lists this as the best packing known; optimality is open.
236
$d_n$:
0.126787767
comment: Packomania [7] lists this as the best packing known; optimality is open.
236
$R_n$:
16.7743925
comment: Packomania [7] lists this as the best packing known; optimality is open.
237
$d_n$:
0.126569619
comment: Packomania [7] lists this as the best packing known; optimality is open.
237
$R_n$:
16.8015803
comment: Packomania [7] lists this as the best packing known; optimality is open.
238
$d_n$:
0.126367063
comment: Packomania [7] lists this as the best packing known; optimality is open.
238
$R_n$:
16.8269090
comment: Packomania [7] lists this as the best packing known; optimality is open.
239
$d_n$:
0.126075538
comment: Packomania [7] lists this as the best packing known; optimality is open.
239
$R_n$:
16.8635056
comment: Packomania [7] lists this as the best packing known; optimality is open.
240
$d_n$:
0.125829911
comment: Packomania [7] lists this as the best packing known; optimality is open.
240
$R_n$:
16.8944721
comment: Packomania [7] lists this as the best packing known; optimality is open.
241
$d_n$:
0.125667099
comment: Packomania [7] lists this as the best packing known; optimality is open.
241
$R_n$:
16.9150646
comment: Packomania [7] lists this as the best packing known; optimality is open.
242
$d_n$:
0.125307719
comment: Packomania [7] lists this as the best packing known; optimality is open.
242
$R_n$:
16.9607087
comment: Packomania [7] lists this as the best packing known; optimality is open.
243
$d_n$:
0.124998063
comment: Packomania [7] lists this as the best packing known; optimality is open.
243
$R_n$:
17.0002480
comment: Packomania [7] lists this as the best packing known; optimality is open.
244
$d_n$:
0.124728665
comment: Packomania [7] lists this as the best packing known; optimality is open.
244
$R_n$:
17.0348064
comment: Packomania [7] lists this as the best packing known; optimality is open.
245
$d_n$:
0.124419202
comment: Packomania [7] lists this as the best packing known; optimality is open.
245
$R_n$:
17.0746892
comment: Packomania [7] lists this as the best packing known; optimality is open.
246
$d_n$:
0.124162505
comment: Packomania [7] lists this as the best packing known; optimality is open.
246
$R_n$:
17.1079225
comment: Packomania [7] lists this as the best packing known; optimality is open.
247
$d_n$:
0.123976658
comment: Packomania [7] lists this as the best packing known; optimality is open.
247
$R_n$:
17.1320689
comment: Packomania [7] lists this as the best packing known; optimality is open.
248
$d_n$:
0.123592834
comment: Packomania [7] lists this as the best packing known; optimality is open.
248
$R_n$:
17.1821679
comment: Packomania [7] lists this as the best packing known; optimality is open.
249
$d_n$:
0.123312149
comment: Packomania [7] lists this as the best packing known; optimality is open.
249
$R_n$:
17.2190021
comment: Packomania [7] lists this as the best packing known; optimality is open.
250
$d_n$:
0.122986444
comment: Packomania [7] lists this as the best packing known; optimality is open.
250
$R_n$:
17.2619548
comment: Packomania [7] lists this as the best packing known; optimality is open.
251
$d_n$:
0.122734099
comment: Packomania [7] lists this as the best packing known; optimality is open.
251
$R_n$:
17.2953899
comment: Packomania [7] lists this as the best packing known; optimality is open.
252
$d_n$:
0.122510015
comment: Packomania [7] lists this as the best packing known; optimality is open.
252
$R_n$:
17.3251959
comment: Packomania [7] lists this as the best packing known; optimality is open.
253
$d_n$:
0.122354532
comment: Packomania [7] lists this as the best packing known; optimality is open.
253
$R_n$:
17.3459413
comment: Packomania [7] lists this as the best packing known; optimality is open.
254
$d_n$:
0.121997848
comment: Packomania [7] lists this as the best packing known; optimality is open.
254
$R_n$:
17.3937318
comment: Packomania [7] lists this as the best packing known; optimality is open.
255
$d_n$:
0.121624825
comment: Packomania [7] lists this as the best packing known; optimality is open.
255
$R_n$:
17.4440114
comment: Packomania [7] lists this as the best packing known; optimality is open.
256
$d_n$:
0.121313206
comment: Packomania [7] lists this as the best packing known; optimality is open.
256
$R_n$:
17.4862513
comment: Packomania [7] lists this as the best packing known; optimality is open.
257
$d_n$:
0.121080304
comment: Packomania [7] lists this as the best packing known; optimality is open.
257
$R_n$:
17.5179632
comment: Packomania [7] lists this as the best packing known; optimality is open.
258
$d_n$:
0.120931883
comment: Packomania [7] lists this as the best packing known; optimality is open.
258
$R_n$:
17.5382358
comment: Packomania [7] lists this as the best packing known; optimality is open.
259
$d_n$:
0.120675570
comment: Packomania [7] lists this as the best packing known; optimality is open.
259
$R_n$:
17.5733627
comment: Packomania [7] lists this as the best packing known; optimality is open.
260
$d_n$:
0.120475864
comment: Packomania [7] lists this as the best packing known; optimality is open.
260
$R_n$:
17.6008355
comment: Packomania [7] lists this as the best packing known; optimality is open.
261
$d_n$:
0.120284540
comment: Packomania [7] lists this as the best packing known; optimality is open.
261
$R_n$:
17.6272407
comment: Packomania [7] lists this as the best packing known; optimality is open.
262
$d_n$:
0.120066255
comment: Packomania [7] lists this as the best packing known; optimality is open.
262
$R_n$:
17.6574697
comment: Packomania [7] lists this as the best packing known; optimality is open.
263
$d_n$:
0.119843022
comment: Packomania [7] lists this as the best packing known; optimality is open.
263
$R_n$:
17.6884977
comment: Packomania [7] lists this as the best packing known; optimality is open.
264
$d_n$:
0.119750627
comment: Packomania [7] lists this as the best packing known; optimality is open.
264
$R_n$:
17.7013739
comment: Packomania [7] lists this as the best packing known; optimality is open.
265
$d_n$:
0.119465572
comment: Packomania [7] lists this as the best packing known; optimality is open.
265
$R_n$:
17.7412248
comment: Packomania [7] lists this as the best packing known; optimality is open.
266
$d_n$:
0.119217314
comment: Packomania [7] lists this as the best packing known; optimality is open.
266
$R_n$:
17.7760868
comment: Packomania [7] lists this as the best packing known; optimality is open.
267
$d_n$:
0.119066393
comment: Packomania [7] lists this as the best packing known; optimality is open.
267
$R_n$:
17.7973511
comment: Packomania [7] lists this as the best packing known; optimality is open.
268
$d_n$:
0.118822175
comment: Packomania [7] lists this as the best packing known; optimality is open.
268
$R_n$:
17.8318750
comment: Packomania [7] lists this as the best packing known; optimality is open.
269
$d_n$:
0.118605818
comment: Packomania [7] lists this as the best packing known; optimality is open.
269
$R_n$:
17.8625793
comment: Packomania [7] lists this as the best packing known; optimality is open.
270
$d_n$:
0.118432435
comment: Packomania [7] lists this as the best packing known; optimality is open.
270
$R_n$:
17.8872657
comment: Packomania [7] lists this as the best packing known; optimality is open.
271
$d_n$:
0.118135765
comment: Packomania [7] lists this as the best packing known; optimality is open.
271
$R_n$:
17.9296741
comment: Packomania [7] lists this as the best packing known; optimality is open.
272
$d_n$:
0.117930163
comment: Packomania [7] lists this as the best packing known; optimality is open.
272
$R_n$:
17.9591897
comment: Packomania [7] lists this as the best packing known; optimality is open.
273
$d_n$:
0.117679598
comment: Packomania [7] lists this as the best packing known; optimality is open.
273
$R_n$:
17.9952993
comment: Packomania [7] lists this as the best packing known; optimality is open.
274
$d_n$:
0.117415095
comment: Packomania [7] lists this as the best packing known; optimality is open.
274
$R_n$:
18.0335850
comment: Packomania [7] lists this as the best packing known; optimality is open.
275
$d_n$:
0.117215061
comment: Packomania [7] lists this as the best packing known; optimality is open.
275
$R_n$:
18.0626537
comment: Packomania [7] lists this as the best packing known; optimality is open.
276
$d_n$:
0.116935701
comment: Packomania [7] lists this as the best packing known; optimality is open.
276
$R_n$:
18.1034165
comment: Packomania [7] lists this as the best packing known; optimality is open.
277
$d_n$:
0.116712818
comment: Packomania [7] lists this as the best packing known; optimality is open.
277
$R_n$:
18.1360784
comment: Packomania [7] lists this as the best packing known; optimality is open.
278
$d_n$:
0.116414259
comment: Packomania [7] lists this as the best packing known; optimality is open.
278
$R_n$:
18.1800260
comment: Packomania [7] lists this as the best packing known; optimality is open.
279
$d_n$:
0.116161765
comment: Packomania [7] lists this as the best packing known; optimality is open.
279
$R_n$:
18.2173692
comment: Packomania [7] lists this as the best packing known; optimality is open.
280
$d_n$:
0.115969437
comment: Packomania [7] lists this as the best packing known; optimality is open.
280
$R_n$:
18.2459231
comment: Packomania [7] lists this as the best packing known; optimality is open.
281
$d_n$:
0.115739370
comment: Packomania [7] lists this as the best packing known; optimality is open.
281
$R_n$:
18.2802046
comment: Packomania [7] lists this as the best packing known; optimality is open.
282
$d_n$:
0.115558351
comment: Packomania [7] lists this as the best packing known; optimality is open.
282
$R_n$:
18.3072737
comment: Packomania [7] lists this as the best packing known; optimality is open.
283
$d_n$:
0.115339699
comment: Packomania [7] lists this as the best packing known; optimality is open.
283
$R_n$:
18.3400833
comment: Packomania [7] lists this as the best packing known; optimality is open.
284
$d_n$:
0.115211168
comment: Packomania [7] lists this as the best packing known; optimality is open.
284
$R_n$:
18.3594282
comment: Packomania [7] lists this as the best packing known; optimality is open.
285
$d_n$:
0.114937835
comment: Packomania [7] lists this as the best packing known; optimality is open.
285
$R_n$:
18.4007106
comment: Packomania [7] lists this as the best packing known; optimality is open.
286
$d_n$:
0.114749685
comment: Packomania [7] lists this as the best packing known; optimality is open.
286
$R_n$:
18.4292417
comment: Packomania [7] lists this as the best packing known; optimality is open.
287
$d_n$:
0.114498749
comment: Packomania [7] lists this as the best packing known; optimality is open.
287
$R_n$:
18.4674398
comment: Packomania [7] lists this as the best packing known; optimality is open.
288
$d_n$:
0.114323041
comment: Packomania [7] lists this as the best packing known; optimality is open.
288
$R_n$:
18.4942862
comment: Packomania [7] lists this as the best packing known; optimality is open.
289
$d_n$:
0.114210768
comment: Packomania [7] lists this as the best packing known; optimality is open.
289
$R_n$:
18.5114836
comment: Packomania [7] lists this as the best packing known; optimality is open.
290
$d_n$:
0.113969043
comment: Packomania [7] lists this as the best packing known; optimality is open.
290
$R_n$:
18.5486250
comment: Packomania [7] lists this as the best packing known; optimality is open.
291
$d_n$:
0.113856045
comment: Packomania [7] lists this as the best packing known; optimality is open.
291
$R_n$:
18.5660414
comment: Packomania [7] lists this as the best packing known; optimality is open.
292
$d_n$:
0.113672944
comment: Packomania [7] lists this as the best packing known; optimality is open.
292
$R_n$:
18.5943363
comment: Packomania [7] lists this as the best packing known; optimality is open.
293
$d_n$:
0.113489418
comment: Packomania [7] lists this as the best packing known; optimality is open.
293
$R_n$:
18.6227885
comment: Packomania [7] lists this as the best packing known; optimality is open.
294
$d_n$:
0.113351219
comment: Packomania [7] lists this as the best packing known; optimality is open.
294
$R_n$:
18.6442743
comment: Packomania [7] lists this as the best packing known; optimality is open.
295
$d_n$:
0.113280961
comment: Packomania [7] lists this as the best packing known; optimality is open.
295
$R_n$:
18.6552175
comment: Packomania [7] lists this as the best packing known; optimality is open.
296
$d_n$:
0.112977912
comment: Packomania [7] lists this as the best packing known; optimality is open.
296
$R_n$:
18.7025753
comment: Packomania [7] lists this as the best packing known; optimality is open.
297
$d_n$:
0.112804592
comment: Packomania [7] lists this as the best packing known; optimality is open.
297
$R_n$:
18.7297747
comment: Packomania [7] lists this as the best packing known; optimality is open.
298
$d_n$:
0.112616768
comment: Packomania [7] lists this as the best packing known; optimality is open.
298
$R_n$:
18.7593447
comment: Packomania [7] lists this as the best packing known; optimality is open.
299
$d_n$:
0.112452698
comment: Packomania [7] lists this as the best packing known; optimality is open.
299
$R_n$:
18.7852558
comment: Packomania [7] lists this as the best packing known; optimality is open.
300
$d_n$:
0.112276581
comment: Packomania [7] lists this as the best packing known; optimality is open.
300
$R_n$:
18.8131537
comment: Packomania [7] lists this as the best packing known; optimality is open.
301
$d_n$:
0.112085863
comment: Packomania [7] lists this as the best packing known; optimality is open.
301
$R_n$:
18.8434635
comment: Packomania [7] lists this as the best packing known; optimality is open.
302
$d_n$:
0.111783166
comment: Packomania [7] lists this as the best packing known; optimality is open.
302
$R_n$:
18.8917816
comment: Packomania [7] lists this as the best packing known; optimality is open.
303
$d_n$:
0.111546748
comment: Packomania [7] lists this as the best packing known; optimality is open.
303
$R_n$:
18.9297024
comment: Packomania [7] lists this as the best packing known; optimality is open.
304
$d_n$:
0.111341591
comment: Packomania [7] lists this as the best packing known; optimality is open.
304
$R_n$:
18.9627396
comment: Packomania [7] lists this as the best packing known; optimality is open.
305
$d_n$:
0.111103498
comment: Packomania [7] lists this as the best packing known; optimality is open.
305
$R_n$:
19.0012334
comment: Packomania [7] lists this as the best packing known; optimality is open.
306
$d_n$:
0.110923838
comment: Packomania [7] lists this as the best packing known; optimality is open.
306
$R_n$:
19.0303894
comment: Packomania [7] lists this as the best packing known; optimality is open.
307
$d_n$:
0.110743122
comment: Packomania [7] lists this as the best packing known; optimality is open.
307
$R_n$:
19.0598124
comment: Packomania [7] lists this as the best packing known; optimality is open.
308
$d_n$:
0.110468663
comment: Packomania [7] lists this as the best packing known; optimality is open.
308
$R_n$:
19.1046819
comment: Packomania [7] lists this as the best packing known; optimality is open.
309
$d_n$:
0.110245505
comment: Packomania [7] lists this as the best packing known; optimality is open.
309
$R_n$:
19.1413292
comment: Packomania [7] lists this as the best packing known; optimality is open.
310
$d_n$:
0.110023635
comment: Packomania [7] lists this as the best packing known; optimality is open.
310
$R_n$:
19.1779123
comment: Packomania [7] lists this as the best packing known; optimality is open.
311
$d_n$:
0.109826579
comment: Packomania [7] lists this as the best packing known; optimality is open.
311
$R_n$:
19.2105280
comment: Packomania [7] lists this as the best packing known; optimality is open.
312
$d_n$:
0.109687696
comment: Packomania [7] lists this as the best packing known; optimality is open.
312
$R_n$:
19.2335857
comment: Packomania [7] lists this as the best packing known; optimality is open.
313
$d_n$:
0.109547055
comment: Packomania [7] lists this as the best packing known; optimality is open.
313
$R_n$:
19.2569947
comment: Packomania [7] lists this as the best packing known; optimality is open.
314
$d_n$:
0.109372153
comment: Packomania [7] lists this as the best packing known; optimality is open.
314
$R_n$:
19.2861902
comment: Packomania [7] lists this as the best packing known; optimality is open.
315
$d_n$:
0.109276039
comment: Packomania [7] lists this as the best packing known; optimality is open.
315
$R_n$:
19.3022740
comment: Packomania [7] lists this as the best packing known; optimality is open.
316
$d_n$:
0.109086694
comment: Packomania [7] lists this as the best packing known; optimality is open.
316
$R_n$:
19.3340418
comment: Packomania [7] lists this as the best packing known; optimality is open.
317
$d_n$:
0.108887414
comment: Packomania [7] lists this as the best packing known; optimality is open.
317
$R_n$:
19.3675957
comment: Packomania [7] lists this as the best packing known; optimality is open.
318
$d_n$:
0.108745497
comment: Packomania [7] lists this as the best packing known; optimality is open.
318
$R_n$:
19.3915661
comment: Packomania [7] lists this as the best packing known; optimality is open.
319
$d_n$:
0.108552423
comment: Packomania [7] lists this as the best packing known; optimality is open.
319
$R_n$:
19.4242778
comment: Packomania [7] lists this as the best packing known; optimality is open.
320
$d_n$:
0.108394000
comment: Packomania [7] lists this as the best packing known; optimality is open.
320
$R_n$:
19.4512057
comment: Packomania [7] lists this as the best packing known; optimality is open.
321
$d_n$:
0.108201327
comment: Packomania [7] lists this as the best packing known; optimality is open.
321
$R_n$:
19.4840616
comment: Packomania [7] lists this as the best packing known; optimality is open.
322
$d_n$:
0.108017018
comment: Packomania [7] lists this as the best packing known; optimality is open.
322
$R_n$:
19.5156009
comment: Packomania [7] lists this as the best packing known; optimality is open.
323
$d_n$:
0.107829955
comment: Packomania [7] lists this as the best packing known; optimality is open.
323
$R_n$:
19.5477218
comment: Packomania [7] lists this as the best packing known; optimality is open.
324
$d_n$:
0.107708372
comment: Packomania [7] lists this as the best packing known; optimality is open.
324
$R_n$:
19.5686588
comment: Packomania [7] lists this as the best packing known; optimality is open.
325
$d_n$:
0.107531266
comment: Packomania [7] lists this as the best packing known; optimality is open.
325
$R_n$:
19.5992417
comment: Packomania [7] lists this as the best packing known; optimality is open.
326
$d_n$:
0.107404337
comment: Packomania [7] lists this as the best packing known; optimality is open.
326
$R_n$:
19.6212220
comment: Packomania [7] lists this as the best packing known; optimality is open.
327
$d_n$:
0.107243315
comment: Packomania [7] lists this as the best packing known; optimality is open.
327
$R_n$:
19.6491810
comment: Packomania [7] lists this as the best packing known; optimality is open.
328
$d_n$:
0.107091523
comment: Packomania [7] lists this as the best packing known; optimality is open.
328
$R_n$:
19.6756144
comment: Packomania [7] lists this as the best packing known; optimality is open.
329
$d_n$:
0.106923084
comment: Packomania [7] lists this as the best packing known; optimality is open.
329
$R_n$:
19.7050348
comment: Packomania [7] lists this as the best packing known; optimality is open.
330
$d_n$:
0.106767393
comment: Packomania [7] lists this as the best packing known; optimality is open.
330
$R_n$:
19.7323109
comment: Packomania [7] lists this as the best packing known; optimality is open.
331
$d_n$:
0.106606370
comment: Packomania [7] lists this as the best packing known; optimality is open.
331
$R_n$:
19.7606051
comment: Packomania [7] lists this as the best packing known; optimality is open.
332
$d_n$:
0.106424823
comment: Packomania [7] lists this as the best packing known; optimality is open.
332
$R_n$:
19.7926082
comment: Packomania [7] lists this as the best packing known; optimality is open.
333
$d_n$:
0.106256694
comment: Packomania [7] lists this as the best packing known; optimality is open.
333
$R_n$:
19.8223436
comment: Packomania [7] lists this as the best packing known; optimality is open.
334
$d_n$:
0.106077470
comment: Packomania [7] lists this as the best packing known; optimality is open.
334
$R_n$:
19.8541449
comment: Packomania [7] lists this as the best packing known; optimality is open.
335
$d_n$:
0.105903600
comment: Packomania [7] lists this as the best packing known; optimality is open.
335
$R_n$:
19.8850992
comment: Packomania [7] lists this as the best packing known; optimality is open.
336
$d_n$:
0.105713865
comment: Packomania [7] lists this as the best packing known; optimality is open.
336
$R_n$:
19.9189941
comment: Packomania [7] lists this as the best packing known; optimality is open.
337
$d_n$:
0.105538643
comment: Packomania [7] lists this as the best packing known; optimality is open.
337
$R_n$:
19.9504047
comment: Packomania [7] lists this as the best packing known; optimality is open.
338
$d_n$:
0.105319901
comment: Packomania [7] lists this as the best packing known; optimality is open.
338
$R_n$:
19.9897633
comment: Packomania [7] lists this as the best packing known; optimality is open.
339
$d_n$:
0.105147705
comment: Packomania [7] lists this as the best packing known; optimality is open.
339
$R_n$:
20.0208622
comment: Packomania [7] lists this as the best packing known; optimality is open.
340
$d_n$:
0.104972095
comment: Packomania [7] lists this as the best packing known; optimality is open.
340
$R_n$:
20.0526826
comment: Packomania [7] lists this as the best packing known; optimality is open.
341
$d_n$:
0.104828893
comment: Packomania [7] lists this as the best packing known; optimality is open.
341
$R_n$:
20.0787095
comment: Packomania [7] lists this as the best packing known; optimality is open.
342
$d_n$:
0.104705652
comment: Packomania [7] lists this as the best packing known; optimality is open.
342
$R_n$:
20.1011656
comment: Packomania [7] lists this as the best packing known; optimality is open.
343
$d_n$:
0.104639446
comment: Packomania [7] lists this as the best packing known; optimality is open.
343
$R_n$:
20.1132510
comment: Packomania [7] lists this as the best packing known; optimality is open.
344
$d_n$:
0.104403381
comment: Packomania [7] lists this as the best packing known; optimality is open.
344
$R_n$:
20.1564677
comment: Packomania [7] lists this as the best packing known; optimality is open.
345
$d_n$:
0.104325776
comment: Packomania [7] lists this as the best packing known; optimality is open.
345
$R_n$:
20.1707177
comment: Packomania [7] lists this as the best packing known; optimality is open.
346
$d_n$:
0.104196674
comment: Packomania [7] lists this as the best packing known; optimality is open.
346
$R_n$:
20.1944706
comment: Packomania [7] lists this as the best packing known; optimality is open.
347
$d_n$:
0.104044210
comment: Packomania [7] lists this as the best packing known; optimality is open.
347
$R_n$:
20.2225979
comment: Packomania [7] lists this as the best packing known; optimality is open.
348
$d_n$:
0.103975651
comment: Packomania [7] lists this as the best packing known; optimality is open.
348
$R_n$:
20.2352727
comment: Packomania [7] lists this as the best packing known; optimality is open.
349
$d_n$:
0.103942494
comment: Packomania [7] lists this as the best packing known; optimality is open.
349
$R_n$:
20.2414087
comment: Packomania [7] lists this as the best packing known; optimality is open.
350
$d_n$:
0.103631587
comment: Packomania [7] lists this as the best packing known; optimality is open.
350
$R_n$:
20.2991352
comment: Packomania [7] lists this as the best packing known; optimality is open.
351
$d_n$:
0.103475079
comment: Packomania [7] lists this as the best packing known; optimality is open.
351
$R_n$:
20.3283253
comment: Packomania [7] lists this as the best packing known; optimality is open.
352
$d_n$:
0.103319351
comment: Packomania [7] lists this as the best packing known; optimality is open.
352
$R_n$:
20.3574581
comment: Packomania [7] lists this as the best packing known; optimality is open.
353
$d_n$:
0.103166426
comment: Packomania [7] lists this as the best packing known; optimality is open.
353
$R_n$:
20.3861519
comment: Packomania [7] lists this as the best packing known; optimality is open.
354
$d_n$:
0.103035319
comment: Packomania [7] lists this as the best packing known; optimality is open.
354
$R_n$:
20.4108196
comment: Packomania [7] lists this as the best packing known; optimality is open.
355
$d_n$:
0.102907703
comment: Packomania [7] lists this as the best packing known; optimality is open.
355
$R_n$:
20.4348911
comment: Packomania [7] lists this as the best packing known; optimality is open.
356
$d_n$:
0.102721872
comment: Packomania [7] lists this as the best packing known; optimality is open.
356
$R_n$:
20.4700502
comment: Packomania [7] lists this as the best packing known; optimality is open.
357
$d_n$:
0.102576419
comment: Packomania [7] lists this as the best packing known; optimality is open.
357
$R_n$:
20.4976587
comment: Packomania [7] lists this as the best packing known; optimality is open.
358
$d_n$:
0.102444128
comment: Packomania [7] lists this as the best packing known; optimality is open.
358
$R_n$:
20.5228368
comment: Packomania [7] lists this as the best packing known; optimality is open.
359
$d_n$:
0.102300193
comment: Packomania [7] lists this as the best packing known; optimality is open.
359
$R_n$:
20.5503053
comment: Packomania [7] lists this as the best packing known; optimality is open.
360
$d_n$:
0.102128845
comment: Packomania [7] lists this as the best packing known; optimality is open.
360
$R_n$:
20.5831059
comment: Packomania [7] lists this as the best packing known; optimality is open.
361
$d_n$:
0.102059002
comment: Packomania [7] lists this as the best packing known; optimality is open.
361
$R_n$:
20.5965076
comment: Packomania [7] lists this as the best packing known; optimality is open.
362
$d_n$:
0.101833424
comment: Packomania [7] lists this as the best packing known; optimality is open.
362
$R_n$:
20.6399170
comment: Packomania [7] lists this as the best packing known; optimality is open.
363
$d_n$:
0.101712462
comment: Packomania [7] lists this as the best packing known; optimality is open.
363
$R_n$:
20.6632739
comment: Packomania [7] lists this as the best packing known; optimality is open.
364
$d_n$:
0.101566956
comment: Packomania [7] lists this as the best packing known; optimality is open.
364
$R_n$:
20.6914438
comment: Packomania [7] lists this as the best packing known; optimality is open.
365
$d_n$:
0.101408289
comment: Packomania [7] lists this as the best packing known; optimality is open.
365
$R_n$:
20.7222538
comment: Packomania [7] lists this as the best packing known; optimality is open.
366
$d_n$:
0.101283497
comment: Packomania [7] lists this as the best packing known; optimality is open.
366
$R_n$:
20.7465536
comment: Packomania [7] lists this as the best packing known; optimality is open.
367
$d_n$:
0.101141292
comment: Packomania [7] lists this as the best packing known; optimality is open.
367
$R_n$:
20.7743173
comment: Packomania [7] lists this as the best packing known; optimality is open.
368
$d_n$:
0.100909588
comment: Packomania [7] lists this as the best packing known; optimality is open.
368
$R_n$:
20.8197221
comment: Packomania [7] lists this as the best packing known; optimality is open.
369
$d_n$:
0.100734566
comment: Packomania [7] lists this as the best packing known; optimality is open.
369
$R_n$:
20.8541582
comment: Packomania [7] lists this as the best packing known; optimality is open.
370
$d_n$:
0.100558466
comment: Packomania [7] lists this as the best packing known; optimality is open.
370
$R_n$:
20.8889272
comment: Packomania [7] lists this as the best packing known; optimality is open.
371
$d_n$:
0.100382788
comment: Packomania [7] lists this as the best packing known; optimality is open.
371
$R_n$:
20.9237343
comment: Packomania [7] lists this as the best packing known; optimality is open.
372
$d_n$:
0.100268761
comment: Packomania [7] lists this as the best packing known; optimality is open.
372
$R_n$:
20.9463919
comment: Packomania [7] lists this as the best packing known; optimality is open.
373
$d_n$:
0.100141276
comment: Packomania [7] lists this as the best packing known; optimality is open.
373
$R_n$:
20.9717848
comment: Packomania [7] lists this as the best packing known; optimality is open.
374
$d_n$:
0.100037879
comment: Packomania [7] lists this as the best packing known; optimality is open.
374
$R_n$:
20.9924271
comment: Packomania [7] lists this as the best packing known; optimality is open.
375
$d_n$:
0.0998883022
comment: Packomania [7] lists this as the best packing known; optimality is open.
375
$R_n$:
21.0223645
comment: Packomania [7] lists this as the best packing known; optimality is open.
376
$d_n$:
0.0998104073
comment: Packomania [7] lists this as the best packing known; optimality is open.
376
$R_n$:
21.0379906
comment: Packomania [7] lists this as the best packing known; optimality is open.
377
$d_n$:
0.0996840637
comment: Packomania [7] lists this as the best packing known; optimality is open.
377
$R_n$:
21.0633875
comment: Packomania [7] lists this as the best packing known; optimality is open.
378
$d_n$:
0.0995544703
comment: Packomania [7] lists this as the best packing known; optimality is open.
378
$R_n$:
21.0895047
comment: Packomania [7] lists this as the best packing known; optimality is open.
379
$d_n$:
0.0994505600
comment: Packomania [7] lists this as the best packing known; optimality is open.
379
$R_n$:
21.1104951
comment: Packomania [7] lists this as the best packing known; optimality is open.
380
$d_n$:
0.0993241547
comment: Packomania [7] lists this as the best packing known; optimality is open.
380
$R_n$:
21.1360888
comment: Packomania [7] lists this as the best packing known; optimality is open.
381
$d_n$:
0.0991828312
comment: Packomania [7] lists this as the best packing known; optimality is open.
381
$R_n$:
21.1647803
comment: Packomania [7] lists this as the best packing known; optimality is open.
382
$d_n$:
0.0990733538
comment: Packomania [7] lists this as the best packing known; optimality is open.
382
$R_n$:
21.1870627
comment: Packomania [7] lists this as the best packing known; optimality is open.
383
$d_n$:
0.0989175517
comment: Packomania [7] lists this as the best packing known; optimality is open.
383
$R_n$:
21.2188587
comment: Packomania [7] lists this as the best packing known; optimality is open.
384
$d_n$:
0.0987639002
comment: Packomania [7] lists this as the best packing known; optimality is open.
384
$R_n$:
21.2503141
comment: Packomania [7] lists this as the best packing known; optimality is open.
385
$d_n$:
0.0985969241
comment: Packomania [7] lists this as the best packing known; optimality is open.
385
$R_n$:
21.2846084
comment: Packomania [7] lists this as the best packing known; optimality is open.
386
$d_n$:
0.0984855444
comment: Packomania [7] lists this as the best packing known; optimality is open.
386
$R_n$:
21.3075488
comment: Packomania [7] lists this as the best packing known; optimality is open.
387
$d_n$:
0.0983279083
comment: Packomania [7] lists this as the best packing known; optimality is open.
387
$R_n$:
21.3401052
comment: Packomania [7] lists this as the best packing known; optimality is open.
388
$d_n$:
0.0982136115
comment: Packomania [7] lists this as the best packing known; optimality is open.
388
$R_n$:
21.3637762
comment: Packomania [7] lists this as the best packing known; optimality is open.
389
$d_n$:
0.0980758096
comment: Packomania [7] lists this as the best packing known; optimality is open.
389
$R_n$:
21.3923884
comment: Packomania [7] lists this as the best packing known; optimality is open.
390
$d_n$:
0.0979317481
comment: Packomania [7] lists this as the best packing known; optimality is open.
390
$R_n$:
21.4223864
comment: Packomania [7] lists this as the best packing known; optimality is open.
391
$d_n$:
0.0978184289
comment: Packomania [7] lists this as the best packing known; optimality is open.
391
$R_n$:
21.4460450
comment: Packomania [7] lists this as the best packing known; optimality is open.
392
$d_n$:
0.0977013249
comment: Packomania [7] lists this as the best packing known; optimality is open.
392
$R_n$:
21.4705515
comment: Packomania [7] lists this as the best packing known; optimality is open.
393
$d_n$:
0.0975695198
comment: Packomania [7] lists this as the best packing known; optimality is open.
393
$R_n$:
21.4982048
comment: Packomania [7] lists this as the best packing known; optimality is open.
394
$d_n$:
0.0974377179
comment: Packomania [7] lists this as the best packing known; optimality is open.
394
$R_n$:
21.5259323
comment: Packomania [7] lists this as the best packing known; optimality is open.
395
$d_n$:
0.0973158279
comment: Packomania [7] lists this as the best packing known; optimality is open.
395
$R_n$:
21.5516414
comment: Packomania [7] lists this as the best packing known; optimality is open.
396
$d_n$:
0.0971886078
comment: Packomania [7] lists this as the best packing known; optimality is open.
396
$R_n$:
21.5785436
comment: Packomania [7] lists this as the best packing known; optimality is open.
397
$d_n$:
0.0970541709
comment: Packomania [7] lists this as the best packing known; optimality is open.
397
$R_n$:
21.6070484
comment: Packomania [7] lists this as the best packing known; optimality is open.
398
$d_n$:
0.0969263615
comment: Packomania [7] lists this as the best packing known; optimality is open.
398
$R_n$:
21.6342214
comment: Packomania [7] lists this as the best packing known; optimality is open.
399
$d_n$:
0.0968107354
comment: Packomania [7] lists this as the best packing known; optimality is open.
399
$R_n$:
21.6588659
comment: Packomania [7] lists this as the best packing known; optimality is open.
400
$d_n$:
0.0966792733
comment: Packomania [7] lists this as the best packing known; optimality is open.
400
$R_n$:
21.6869573
comment: Packomania [7] lists this as the best packing known; optimality is open.
401
$d_n$:
0.0965664256
comment: Packomania [7] lists this as the best packing known; optimality is open.
401
$R_n$:
21.7111321
comment: Packomania [7] lists this as the best packing known; optimality is open.
402
$d_n$:
0.0964829810
comment: Packomania [7] lists this as the best packing known; optimality is open.
402
$R_n$:
21.7290444
comment: Packomania [7] lists this as the best packing known; optimality is open.
403
$d_n$:
0.0962944534
comment: Packomania [7] lists this as the best packing known; optimality is open.
403
$R_n$:
21.7696283
comment: Packomania [7] lists this as the best packing known; optimality is open.
404
$d_n$:
0.0961350919
comment: Packomania [7] lists this as the best packing known; optimality is open.
404
$R_n$:
21.8040577
comment: Packomania [7] lists this as the best packing known; optimality is open.
405
$d_n$:
0.0960450358
comment: Packomania [7] lists this as the best packing known; optimality is open.
405
$R_n$:
21.8235645
comment: Packomania [7] lists this as the best packing known; optimality is open.
406
$d_n$:
0.0959593914
comment: Packomania [7] lists this as the best packing known; optimality is open.
406
$R_n$:
21.8421497
comment: Packomania [7] lists this as the best packing known; optimality is open.
407
$d_n$:
0.0958696600
comment: Packomania [7] lists this as the best packing known; optimality is open.
407
$R_n$:
21.8616574
comment: Packomania [7] lists this as the best packing known; optimality is open.
408
$d_n$:
0.0958070162
comment: Packomania [7] lists this as the best packing known; optimality is open.
408
$R_n$:
21.8752979
comment: Packomania [7] lists this as the best packing known; optimality is open.
409
$d_n$:
0.0957470288
comment: Packomania [7] lists this as the best packing known; optimality is open.
409
$R_n$:
21.8883766
comment: Packomania [7] lists this as the best packing known; optimality is open.
410
$d_n$:
0.0955940019
comment: Packomania [7] lists this as the best packing known; optimality is open.
410
$R_n$:
21.9218148
comment: Packomania [7] lists this as the best packing known; optimality is open.
411
$d_n$:
0.0955194058
comment: Packomania [7] lists this as the best packing known; optimality is open.
411
$R_n$:
21.9381537
comment: Packomania [7] lists this as the best packing known; optimality is open.
412
$d_n$:
0.0954192864
comment: Packomania [7] lists this as the best packing known; optimality is open.
412
$R_n$:
21.9601232
comment: Packomania [7] lists this as the best packing known; optimality is open.
413
$d_n$:
0.0952958394
comment: Packomania [7] lists this as the best packing known; optimality is open.
413
$R_n$:
21.9872751
comment: Packomania [7] lists this as the best packing known; optimality is open.
414
$d_n$:
0.0952128129
comment: Packomania [7] lists this as the best packing known; optimality is open.
414
$R_n$:
22.0055762
comment: Packomania [7] lists this as the best packing known; optimality is open.
415
$d_n$:
0.0951654650
comment: Packomania [7] lists this as the best packing known; optimality is open.
415
$R_n$:
22.0160272
comment: Packomania [7] lists this as the best packing known; optimality is open.
416
$d_n$:
0.0949987648
comment: Packomania [7] lists this as the best packing known; optimality is open.
416
$R_n$:
22.0529053
comment: Packomania [7] lists this as the best packing known; optimality is open.
417
$d_n$:
0.0949109099
comment: Packomania [7] lists this as the best packing known; optimality is open.
417
$R_n$:
22.0723931
comment: Packomania [7] lists this as the best packing known; optimality is open.
418
$d_n$:
0.0948043382
comment: Packomania [7] lists this as the best packing known; optimality is open.
418
$R_n$:
22.0960810
comment: Packomania [7] lists this as the best packing known; optimality is open.
419
$d_n$:
0.0947029751
comment: Packomania [7] lists this as the best packing known; optimality is open.
419
$R_n$:
22.1186607
comment: Packomania [7] lists this as the best packing known; optimality is open.
420
$d_n$:
0.0946282691
comment: Packomania [7] lists this as the best packing known; optimality is open.
420
$R_n$:
22.1353332
comment: Packomania [7] lists this as the best packing known; optimality is open.
421
$d_n$:
0.0946087981
comment: Packomania [7] lists this as the best packing known; optimality is open.
421
$R_n$:
22.1396830
comment: Packomania [7] lists this as the best packing known; optimality is open.
422
$d_n$:
0.0942954346
comment: Packomania [7] lists this as the best packing known; optimality is open.
422
$R_n$:
22.2099346
comment: Packomania [7] lists this as the best packing known; optimality is open.
423
$d_n$:
0.0941125883
comment: Packomania [7] lists this as the best packing known; optimality is open.
423
$R_n$:
22.2511422
comment: Packomania [7] lists this as the best packing known; optimality is open.
424
$d_n$:
0.0939558772
comment: Packomania [7] lists this as the best packing known; optimality is open.
424
$R_n$:
22.2865875
comment: Packomania [7] lists this as the best packing known; optimality is open.
425
$d_n$:
0.0938536707
comment: Packomania [7] lists this as the best packing known; optimality is open.
425
$R_n$:
22.3097685
comment: Packomania [7] lists this as the best packing known; optimality is open.
426
$d_n$:
0.0937311214
comment: Packomania [7] lists this as the best packing known; optimality is open.
426
$R_n$:
22.3376301
comment: Packomania [7] lists this as the best packing known; optimality is open.
427
$d_n$:
0.0936091732
comment: Packomania [7] lists this as the best packing known; optimality is open.
427
$R_n$:
22.3654275
comment: Packomania [7] lists this as the best packing known; optimality is open.
428
$d_n$:
0.0934761458
comment: Packomania [7] lists this as the best packing known; optimality is open.
428
$R_n$:
22.3958329
comment: Packomania [7] lists this as the best packing known; optimality is open.
429
$d_n$:
0.0933568963
comment: Packomania [7] lists this as the best packing known; optimality is open.
429
$R_n$:
22.4231629
comment: Packomania [7] lists this as the best packing known; optimality is open.
430
$d_n$:
0.0932342652
comment: Packomania [7] lists this as the best packing known; optimality is open.
430
$R_n$:
22.4513408
comment: Packomania [7] lists this as the best packing known; optimality is open.
431
$d_n$:
0.0930843574
comment: Packomania [7] lists this as the best packing known; optimality is open.
431
$R_n$:
22.4858872
comment: Packomania [7] lists this as the best packing known; optimality is open.
432
$d_n$:
0.0929572585
comment: Packomania [7] lists this as the best packing known; optimality is open.
432
$R_n$:
22.5152644
comment: Packomania [7] lists this as the best packing known; optimality is open.
433
$d_n$:
0.0928605486
comment: Packomania [7] lists this as the best packing known; optimality is open.
433
$R_n$:
22.5376716
comment: Packomania [7] lists this as the best packing known; optimality is open.
434
$d_n$:
0.0926936220
comment: Packomania [7] lists this as the best packing known; optimality is open.
434
$R_n$:
22.5764576
comment: Packomania [7] lists this as the best packing known; optimality is open.
435
$d_n$:
0.0925895793
comment: Packomania [7] lists this as the best packing known; optimality is open.
435
$R_n$:
22.6007030
comment: Packomania [7] lists this as the best packing known; optimality is open.
436
$d_n$:
0.0924967244
comment: Packomania [7] lists this as the best packing known; optimality is open.
436
$R_n$:
22.6223873
comment: Packomania [7] lists this as the best packing known; optimality is open.
437
$d_n$:
0.0923541571
comment: Packomania [7] lists this as the best packing known; optimality is open.
437
$R_n$:
22.6557658
comment: Packomania [7] lists this as the best packing known; optimality is open.
438
$d_n$:
0.0922733903
comment: Packomania [7] lists this as the best packing known; optimality is open.
438
$R_n$:
22.6747211
comment: Packomania [7] lists this as the best packing known; optimality is open.
439
$d_n$:
0.0921709130
comment: Packomania [7] lists this as the best packing known; optimality is open.
439
$R_n$:
22.6988194
comment: Packomania [7] lists this as the best packing known; optimality is open.
440
$d_n$:
0.0920737177
comment: Packomania [7] lists this as the best packing known; optimality is open.
440
$R_n$:
22.7217253
comment: Packomania [7] lists this as the best packing known; optimality is open.
441
$d_n$:
0.0919899417
comment: Packomania [7] lists this as the best packing known; optimality is open.
441
$R_n$:
22.7415074
comment: Packomania [7] lists this as the best packing known; optimality is open.
442
$d_n$:
0.0918777279
comment: Packomania [7] lists this as the best packing known; optimality is open.
442
$R_n$:
22.7680612
comment: Packomania [7] lists this as the best packing known; optimality is open.
443
$d_n$:
0.0917825063
comment: Packomania [7] lists this as the best packing known; optimality is open.
443
$R_n$:
22.7906449
comment: Packomania [7] lists this as the best packing known; optimality is open.
444
$d_n$:
0.0916863299
comment: Packomania [7] lists this as the best packing known; optimality is open.
444
$R_n$:
22.8135026
comment: Packomania [7] lists this as the best packing known; optimality is open.
445
$d_n$:
0.0915785976
comment: Packomania [7] lists this as the best packing known; optimality is open.
445
$R_n$:
22.8391639
comment: Packomania [7] lists this as the best packing known; optimality is open.
446
$d_n$:
0.0914963493
comment: Packomania [7] lists this as the best packing known; optimality is open.
446
$R_n$:
22.8587956
comment: Packomania [7] lists this as the best packing known; optimality is open.
447
$d_n$:
0.0913863229
comment: Packomania [7] lists this as the best packing known; optimality is open.
447
$R_n$:
22.8851130
comment: Packomania [7] lists this as the best packing known; optimality is open.
448
$d_n$:
0.0913107329
comment: Packomania [7] lists this as the best packing known; optimality is open.
448
$R_n$:
22.9032302
comment: Packomania [7] lists this as the best packing known; optimality is open.
449
$d_n$:
0.0912076284
comment: Packomania [7] lists this as the best packing known; optimality is open.
449
$R_n$:
22.9279904
comment: Packomania [7] lists this as the best packing known; optimality is open.
450
$d_n$:
0.0911320251
comment: Packomania [7] lists this as the best packing known; optimality is open.
450
$R_n$:
22.9461819
comment: Packomania [7] lists this as the best packing known; optimality is open.
451
$d_n$:
0.0910183568
comment: Packomania [7] lists this as the best packing known; optimality is open.
451
$R_n$:
22.9735894
comment: Packomania [7] lists this as the best packing known; optimality is open.
452
$d_n$:
0.0909383625
comment: Packomania [7] lists this as the best packing known; optimality is open.
452
$R_n$:
22.9929186
comment: Packomania [7] lists this as the best packing known; optimality is open.
453
$d_n$:
0.0908911784
comment: Packomania [7] lists this as the best packing known; optimality is open.
453
$R_n$:
23.0043357
comment: Packomania [7] lists this as the best packing known; optimality is open.
454
$d_n$:
0.0906928159
comment: Packomania [7] lists this as the best packing known; optimality is open.
454
$R_n$:
23.0524634
comment: Packomania [7] lists this as the best packing known; optimality is open.
455
$d_n$:
0.0906023668
comment: Packomania [7] lists this as the best packing known; optimality is open.
455
$R_n$:
23.0744785
comment: Packomania [7] lists this as the best packing known; optimality is open.
456
$d_n$:
0.0904864234
comment: Packomania [7] lists this as the best packing known; optimality is open.
456
$R_n$:
23.1027633
comment: Packomania [7] lists this as the best packing known; optimality is open.
457
$d_n$:
0.0903780799
comment: Packomania [7] lists this as the best packing known; optimality is open.
457
$R_n$:
23.1292597
comment: Packomania [7] lists this as the best packing known; optimality is open.
458
$d_n$:
0.0902961025
comment: Packomania [7] lists this as the best packing known; optimality is open.
458
$R_n$:
23.1493502
comment: Packomania [7] lists this as the best packing known; optimality is open.
459
$d_n$:
0.0902050048
comment: Packomania [7] lists this as the best packing known; optimality is open.
459
$R_n$:
23.1717188
comment: Packomania [7] lists this as the best packing known; optimality is open.
460
$d_n$:
0.0900319004
comment: Packomania [7] lists this as the best packing known; optimality is open.
460
$R_n$:
23.2143484
comment: Packomania [7] lists this as the best packing known; optimality is open.
461
$d_n$:
0.0899204620
comment: Packomania [7] lists this as the best packing known; optimality is open.
461
$R_n$:
23.2418786
comment: Packomania [7] lists this as the best packing known; optimality is open.
462
$d_n$:
0.0898702527
comment: Packomania [7] lists this as the best packing known; optimality is open.
462
$R_n$:
23.2543048
comment: Packomania [7] lists this as the best packing known; optimality is open.
463
$d_n$:
0.0897360886
comment: Packomania [7] lists this as the best packing known; optimality is open.
463
$R_n$:
23.2875772
comment: Packomania [7] lists this as the best packing known; optimality is open.
464
$d_n$:
0.0896289087
comment: Packomania [7] lists this as the best packing known; optimality is open.
464
$R_n$:
23.3142291
comment: Packomania [7] lists this as the best packing known; optimality is open.
465
$d_n$:
0.0895130350
comment: Packomania [7] lists this as the best packing known; optimality is open.
465
$R_n$:
23.3431146
comment: Packomania [7] lists this as the best packing known; optimality is open.
466
$d_n$:
0.0894173222
comment: Packomania [7] lists this as the best packing known; optimality is open.
466
$R_n$:
23.3670308
comment: Packomania [7] lists this as the best packing known; optimality is open.
467
$d_n$:
0.0893309921
comment: Packomania [7] lists this as the best packing known; optimality is open.
467
$R_n$:
23.3886465
comment: Packomania [7] lists this as the best packing known; optimality is open.
468
$d_n$:
0.0892146478
comment: Packomania [7] lists this as the best packing known; optimality is open.
468
$R_n$:
23.4178434
comment: Packomania [7] lists this as the best packing known; optimality is open.
469
$d_n$:
0.0890976607
comment: Packomania [7] lists this as the best packing known; optimality is open.
469
$R_n$:
23.4472785
comment: Packomania [7] lists this as the best packing known; optimality is open.
470
$d_n$:
0.0890086529
comment: Packomania [7] lists this as the best packing known; optimality is open.
470
$R_n$:
23.4697255
comment: Packomania [7] lists this as the best packing known; optimality is open.
471
$d_n$:
0.0889105315
comment: Packomania [7] lists this as the best packing known; optimality is open.
471
$R_n$:
23.4945230
comment: Packomania [7] lists this as the best packing known; optimality is open.
472
$d_n$:
0.0888397054
comment: Packomania [7] lists this as the best packing known; optimality is open.
472
$R_n$:
23.5124565
comment: Packomania [7] lists this as the best packing known; optimality is open.
473
$d_n$:
0.0887177472
comment: Packomania [7] lists this as the best packing known; optimality is open.
473
$R_n$:
23.5434038
comment: Packomania [7] lists this as the best packing known; optimality is open.
474
$d_n$:
0.0886305506
comment: Packomania [7] lists this as the best packing known; optimality is open.
474
$R_n$:
23.5655825
comment: Packomania [7] lists this as the best packing known; optimality is open.
475
$d_n$:
0.0885926413
comment: Packomania [7] lists this as the best packing known; optimality is open.
475
$R_n$:
23.5752384
comment: Packomania [7] lists this as the best packing known; optimality is open.
476
$d_n$:
0.0884923598
comment: Packomania [7] lists this as the best packing known; optimality is open.
476
$R_n$:
23.6008212
comment: Packomania [7] lists this as the best packing known; optimality is open.
477
$d_n$:
0.0884588374
comment: Packomania [7] lists this as the best packing known; optimality is open.
477
$R_n$:
23.6093860
comment: Packomania [7] lists this as the best packing known; optimality is open.
478
$d_n$:
0.0884086112
comment: Packomania [7] lists this as the best packing known; optimality is open.
478
$R_n$:
23.6222307
comment: Packomania [7] lists this as the best packing known; optimality is open.
479
$d_n$:
0.0883643660
comment: Packomania [7] lists this as the best packing known; optimality is open.
479
$R_n$:
23.6335580
comment: Packomania [7] lists this as the best packing known; optimality is open.
480
$d_n$:
0.0883311626
comment: Packomania [7] lists this as the best packing known; optimality is open.
480
$R_n$:
23.6420659
comment: Packomania [7] lists this as the best packing known; optimality is open.
481
$d_n$:
0.0883172167
comment: Packomania [7] lists this as the best packing known; optimality is open.
481
$R_n$:
23.6456412
comment: Packomania [7] lists this as the best packing known; optimality is open.
482
$d_n$:
0.0881109550
comment: Packomania [7] lists this as the best packing known; optimality is open.
482
$R_n$:
23.6986531
comment: Packomania [7] lists this as the best packing known; optimality is open.
483
$d_n$:
0.0880231012
comment: Packomania [7] lists this as the best packing known; optimality is open.
483
$R_n$:
23.7213081
comment: Packomania [7] lists this as the best packing known; optimality is open.
484
$d_n$:
0.0879470007
comment: Packomania [7] lists this as the best packing known; optimality is open.
484
$R_n$:
23.7409688
comment: Packomania [7] lists this as the best packing known; optimality is open.
485
$d_n$:
0.0878553105
comment: Packomania [7] lists this as the best packing known; optimality is open.
485
$R_n$:
23.7647024
comment: Packomania [7] lists this as the best packing known; optimality is open.
486
$d_n$:
0.0877829797
comment: Packomania [7] lists this as the best packing known; optimality is open.
486
$R_n$:
23.7834599
comment: Packomania [7] lists this as the best packing known; optimality is open.
487
$d_n$:
0.0876941069
comment: Packomania [7] lists this as the best packing known; optimality is open.
487
$R_n$:
23.8065496
comment: Packomania [7] lists this as the best packing known; optimality is open.
488
$d_n$:
0.0875822099
comment: Packomania [7] lists this as the best packing known; optimality is open.
488
$R_n$:
23.8356878
comment: Packomania [7] lists this as the best packing known; optimality is open.
489
$d_n$:
0.0875329166
comment: Packomania [7] lists this as the best packing known; optimality is open.
489
$R_n$:
23.8485475
comment: Packomania [7] lists this as the best packing known; optimality is open.
490
$d_n$:
0.0874536612
comment: Packomania [7] lists this as the best packing known; optimality is open.
490
$R_n$:
23.8692541
comment: Packomania [7] lists this as the best packing known; optimality is open.
491
$d_n$:
0.0873479827
comment: Packomania [7] lists this as the best packing known; optimality is open.
491
$R_n$:
23.8969226
comment: Packomania [7] lists this as the best packing known; optimality is open.
492
$d_n$:
0.0872457058
comment: Packomania [7] lists this as the best packing known; optimality is open.
492
$R_n$:
23.9237643
comment: Packomania [7] lists this as the best packing known; optimality is open.
493
$d_n$:
0.0871772948
comment: Packomania [7] lists this as the best packing known; optimality is open.
493
$R_n$:
23.9417534
comment: Packomania [7] lists this as the best packing known; optimality is open.
494
$d_n$:
0.0870900673
comment: Packomania [7] lists this as the best packing known; optimality is open.
494
$R_n$:
23.9647314
comment: Packomania [7] lists this as the best packing known; optimality is open.
495
$d_n$:
0.0869943679
comment: Packomania [7] lists this as the best packing known; optimality is open.
495
$R_n$:
23.9899941
comment: Packomania [7] lists this as the best packing known; optimality is open.
496
$d_n$:
0.0869086676
comment: Packomania [7] lists this as the best packing known; optimality is open.
496
$R_n$:
24.0126644
comment: Packomania [7] lists this as the best packing known; optimality is open.
497
$d_n$:
0.0867723631
comment: Packomania [7] lists this as the best packing known; optimality is open.
497
$R_n$:
24.0488133
comment: Packomania [7] lists this as the best packing known; optimality is open.
498
$d_n$:
0.0867508206
comment: Packomania [7] lists this as the best packing known; optimality is open.
498
$R_n$:
24.0545370
comment: Packomania [7] lists this as the best packing known; optimality is open.
499
$d_n$:
0.0867279990
comment: Packomania [7] lists this as the best packing known; optimality is open.
499
$R_n$:
24.0606035
comment: Packomania [7] lists this as the best packing known; optimality is open.
500
$d_n$:
0.0864641987
comment: Packomania [7] lists this as the best packing known; optimality is open.
500
$R_n$:
24.1309609
comment: Packomania [7] lists this as the best packing known; optimality is open.
Definition
For each integer $n\geq2$, $d_n$ is the largest possible minimum distance among $n$ points in the unit disk. The table also stores $R_n=1+2/d_n$, the enclosing radius for $n$ non-overlapping unit circles. Thus each packing value is listed in two invertible normalisations.
Parameters
$n$
—   number of circles ($n\geq2$)
normalisation
—   whether the row holds the separation $d_n$ or the enclosing radius $R_n$ (either separation or container)
Formulas
(1)
$R_n=1+2/d_n$.
(2)
If $\rho_n$ is the radius of each equal circle inside the unit disk, then $d_n=2\rho_n/(1-\rho_n)$ and $R_n=1/\rho_n$.
Comments
(3)
The separation rows measure points in the unit disk. The container rows use unit small circles and give the radius of the enclosing circle.
(4)
The source files copied from Packomania [7] are from its 25-Dec-2024 update. Packomania marks proven rows by bold radius; the proof status for $n=14$ follows Ekanayake and LaFountain [5].
(5)
Optimality is proven for $2\leq n\leq14$ and for $n=19$. For every other $n$, the stored value is the best packing known from Packomania and optimality is open.
Programs
(P1)
Sage
import numberdb.sage as numberdb
from sage.rings.real_arb import RealBallField

RBF = RealBallField(numberdb.bits(100, losing=96))
d3 = RBF(3).sqrt()
R3 = RBF(1) + RBF(2) / d3
d3, R3
References
[1]
U. Pirl, Der Mindestabstand von n in der Einheitskreisscheibe gelegenen Punkten, Mathematische Nachrichten 40 (1969), 111-124.
[2]
H. Melissen, Densest packing of eleven congruent circles in a circle, Geometriae Dedicata 50 (1994), 15-25.
[3]
F. Fodor, The densest packing of 12 congruent circles in a circle, Contributions to Algebra and Geometry 41 (2000), 401-409.
[4]
F. Fodor, The densest packing of 13 congruent circles in a circle, Contributions to Algebra and Geometry 44 (2003), no. 2, 431-440.
[5]
Dinesh B. Ekanayake and Douglas J. LaFountain, Tight partitions for packing circles in a circle, Italian Journal of Pure and Applied Mathematics 51 (2024), 115-136.
[6]
F. Fodor, The densest packing of 19 congruent circles in a circle, Geometriae Dedicata 74 (1999), 139-145.
Links
Similar tables
Densities of the densest known lattice sphere packings —   another packing table, for infinite lattice sphere packings rather than equal circles in a finite disk
Packing densities and Hermite numbers of the classical lattices —   stores packing densities and Hermite numbers for named lattices rather than a best known finite configuration for each $n$
Kissing numbers —   another finite extremal packing problem, counting unit spheres tangent to one central unit sphere
Data properties
Entries are of type: real number
How well the digits are known: heuristic (agreement-checked)
Table is complete: no (it holds both normalisations for every $2\leq n\leq500$ from Packomania's 25-Dec-2024 source files; optimality is proven for $2\leq n\leq14$ and for $n=19$, and Packomania gives values beyond this range)
How they were obtained:

The closed-form rows $n=2,3,4,5,6,7,8,9,11,13,18,19$ are computed in Sage real balls with arb at numberdb.bits(digits, losing=96) bits. The other rows are Packomania source values rounded to 9 significant digits, the largest precision at which the copied radius, distance and ratio columns agree for every $2\leq n\leq500$.

more

The closed-form rows were compared with Packomania's distance and ratio columns. Optimality is proven by Pirl for $2\leq n\leq10$ [1], by Melissen for $n=11$ [2], by Fodor for $n=12$, $n=13$ and $n=19$ [3] [4] [6], and by Ekanayake and LaFountain for $n=14$ [5].



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