Master Table of Optimum Solutions

Table VII: Optimum Solutions Geometric Problem
N	R	Average Distance	Classes of Equivalent Points	Inertia
2	1	2.0000000000000000	[2]	-
3	1	1.7320508075688770	[3]	[2]
4	1	1.6329931618554520	[4]	[3]
5	1	1.5681433796945200	[3,2]	[1,2]
6	1	1.5313708498984760	[6]	[3]
7	1	1.5014726537771140	[2,2,2,1]	[1,1,1]
8	1	1.4811818238850570	[8]	[2,1]
9	1	1.4651009488737240	[6,3]	[2,1]
10	1	1.4522164530396580	[8,2]	[1,2]
11	1	1.4413588836831470	[4,2,2,2,1]	[1,1,1]
12	1	1.4330744731556120	[12]	[3]
13	1	1.4252615431695770	[4,2,2,2,2,1]	[1,1,1]
14	1	1.4189053199996400	[12,2]	[2,1]
15	1	1.4133392709400530	[6,6,3]	[1,2]
16	1	1.4084926686812280	[12,4]	[3]
16	3	1.4084865353655320	[8,8]	[3]
17	1	1.4042079178076430	[10,5,2]	[1,2]
18	1	1.4003987627110520	[8,8,2]	[2,1]
19	1	1.3969141223780570	[4,4,4,2,2,2,1]	[1,1,1]
20	1	1.3938744790435510	[6,6,6,2]	[2,1]
21	1	1.3910744914194840	[4,4,4,4,2,2,1]	[1]
22	1	1.3885408118392390	[12,6,4]	[]
22	3	1.3885334739916260	[10,10,2]	[]
23	1	1.3861780867255570	[6,6,6,3,2]	[]
24	1	1.3840755088228470	[24]	[]
25	1	1.3820821274471200	[2,2,2,2,2,2,2,2,2,2,1,1,1,1,1]	[]
26	1	1.3802635099547190	[2,2,2,2,2,2,2,2,2,2,2,2,2]	[]
27	1	1.3785991667097890	[10,10,5,2]	[]
28	1	1.3770234821306300	[12,12,4]	[]
29	1	1.3755472857760810	[4,4,4,4,2,2,2,2,2,2,1]	[]
30	1	1.3741907355713900	[4,4,4,4,4,4,4,4]	[3]
31	1	1.3729095285468290	[6,6,3,3,3,3,3,3,1]	[]
32	1	1.3717316397758120	[20,12]	[]
32	8	1.3716956745111910	[8,8,8,8]	[]
33	1	1.3705770053483160	[2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]	[]
33	3	1.3705767016463990	[2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1]	[]
34	1	1.3695152122906170	[4,4,4,4,4,4,4,4,2]	[]
34	22	1.3694977027532800	[8,8,8,8,2]	[]
35	1	1.3685079945692500	[2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1]	[]
36	1	1.3675618275034530	[4,4,4,4,4,4,4,4,4]	[]
37	1	1.3666635549129760	[10,10,10,5,2]	[]
37	2	1.3666623076020220	[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1]	[]
38	1	1.3658129134113220	[12,12,12,2]	[]
38	2	1.3658113185538660	[4,4,4,4,4,4,2,2,2,2,2,2,2]	[]
39	1	1.3650045605591330	[12,6,6,6,6,3]	[]
39	3	1.3650002896529400	[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1]	[]
39	4	1.3650002791136510	[4,4,4,4,4,4,2,2,2,2,2,2,2,1]	[]
40	1	1.3642361802215640	[12,12,12,4]	[]
40	2	1.3642329219438200	[4,4,4,4,4,4,4,4,4,4]	[]
41	1	1.3635030381161380	[12,6,6,6,6,3,2]	[]
41	2	1.3634997149923720	[6,6,6,6,6,6,3,2]	[]
42	1	1.3628053343404460	[10,10,10,10,2]	[]
42	2	1.3628015107516900	[6,6,6,6,6,6,6]	[]
43	1	1.3621380703427890	[2,2,2...2,2,1,1,1,1,1,1,1,1,1]	[]
44	1	1.3615051498142490	[24,12,8]	[]
45	1	1.3608952658493690	[6,6,6,6,6,6,6,3]	[]
46	1	1.3603096339840720	[12,12,12,6,4]	[]
46	2	1.3603093704894270	[4,4,4,4,4,4,4,4,2,2,2,2,2,2,1,1]	[]
46	4	1.3603089935877500	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1]	[]
46	27	1.3603048305280240	[4,4,4,4,4,4,4,4,4,2,2,2,2,2]	[]
47	1	1.3597491587517740	[2,2,2...2,2,1,1,1,1,1,1,1]	[]
47	6	1.3597481645868440	[4,4,4,4,4,4,4,2,2,2,2,2,2,2,2,2,1]	[]
47	9	1.3597480899700270	[2,2,2...2,2,1]	[]
48	1	1.3592207739352030	[24,24]	[]
49	1	1.3587018406909290	[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1]	[]
50	1	1.3582104180883810	[12,12,12,12,2]	[]
51	1	1.3577348849436610	[6,6,6,6,6,6,6,6,3]	[]
51	8	1.3577305638620690	[4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,2,2,1]	[]
52	1	1.3572769812230370	[3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1]	[]
52	2	1.3572768592515670	[4,4,4,4,4,4,4,4,4,4,4,4,4]	[]
52	5	1.3572764713428280	[12,12,12,12,4]	[]
52	7	1.3572764477796940	[2,2,2...2,2]	[]
53	1	1.3568370620992010	[2,2,2...2,2,1]	[]
53	2	1.3568368850701220	[2,2,2...2,2,1]	[]
54	1	1.3564139213533290	[2,2,2...2,2]	[]
54	2	1.3564137108524840	[4,4,4,4,4,4,4,4,4,4,4,4,4,2]	[]
54	4	1.3564136477638840	[6,6,6,6,6,6,6,6,6]	[]
55	1	1.3560046454295050	[2,2,2...2,2,1]	[]
55	2	1.3560044580517130	[4,4,4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,1]	[]
55	4	1.3560043315467440	[2,2,2...2,2,1]	[]
55	5	1.3560042566176660	[1,1,1...1,1]	[]
55	7	1.3560042284604980	[2,2,2...2,2,1]	[]
56	1	1.3556111625446280	[2,2,2...2,2]	[]
56	4	1.3556110812448840	[4,4,4,4,4,4,4,4,4,4,4,4,4,4]	[]
57	1	1.3552303372264860	[6,6,6,6,6,6,6,6,6,3]	[]
58	1	1.3548622937935090	[4,4,4,4,4,4,4,4,4,4,4,4,4,4,2]	[]
58	2	1.3548620245760910	[4,4,4,4,4,4,4,4,4,4,4,4,4,4,2]	[]
58	4	1.3548619264242830	[2,2,2...2,2]	[]
58	10	1.3548615946844230	[1,1,1...1,1]	[]
58	15	1.3548614704580290	[3,3,3...3,3,1]	[]
58	20	1.3548613222300270	[2,2,2...2,2]	[]
58	87	1.3548588792978410	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1]	[]
59	1	1.3545070695344310	[2,2,2...2,2,1]	[]
59	2	1.3545069692497680	[1,1,1...1,1]	[]
59	5	1.3545068886037400	[2,2,2...2,2,1,1,1,1,1,1,1,1,1]	[]
59	8	1.3545067559183490	[2,2,2...2,2,1]	[]
60	1	1.3541648570480110	[6,6,6,6,6,6,6,6,6,6]	[]
60	2	1.3541648022199600	[2,2,2...2,2]	[]
60	2	1.3541648022199600	[2,2,2...2,2]	[]
60	3	1.3541647617392100	[3,3,3...3,3]	[]
61	1	1.3538309038298360	[1,1,1...1,1]	[]
61	7	1.3538307140830010	[2,2,2...2,2,1]	[]
61	9	1.3538306842325470	[2,2,2...2,2,1]	[]
61	21	1.3538300346934530	[1,1,1...1,1]	[]
62	1	1.3535100346924970	[10,10,10,10,10,10,2]	[]
63	1	1.3531974859205240	[6,6,6,6,6,6,6,6,6,6,3]	[]
64	1	1.3528945024124690	[4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4]	[]
64	3	1.3528942541796940	[8,8,8,8,8,8,4,4,4,4]	[]
64	4	1.3528941916857390	[2,2,2...2,2]	[]
64	16	1.3528929513075850	[16,8,8,8,8,8,8]	[]
65	1	1.3526008028140160	[2,2,2...2,2,1]	[]
65	5	1.3526002347482880	[6,6,6,6,6,6,6,6,6,6,3,2]	[]
65	13	1.3526000083351290	[1,1,1...1,1]	[]
66	1	1.3523170635430120	[6,6,6,6,6,6,6,6,6,6,6]	[]
66	1	1.3523169500944200	[2,2,2...2,2]	[]
66	1	1.3523169155560030	[2,2,2...2,2]	[]
67	1	1.3520418470608080	[10,10,10,10,10,10,5,2]	[]
68	1	1.3517727307495290	[4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4]	[]
68	1	1.3517725475384190	[6,6,6,6,6,6,6,6,6,6,6,2]	[]
68	1	1.3511403427571050	[1,1,1...1,1]	[]
69	1	1.3515120695316500	[6,6,6,6,6,6,6,6,6,6,6,3]	[]
69	2	1.3515120143129190	[6,6,6,6,6,6,6,6,6,6,6,3]	[]
69	4	1.3515115916764310	[4,4,4,4,4,4,4,4,4,4,4,4,4,2,2,2,2,2,2,2,2,1]	[]
70	1	1.3512591887543760	[4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,2]	[]
70	1	1.3512574692313020	[2,2,2...2,2]	[]
71	1	1.3510128897583190	[2,2,2...2,2,1]	[]
71	1	1.3510113994533960	[1,1,1...1,1]	[]
72	1	1.3507755607893160	[10,10,10,10,10,10,10,2]	[]
72	1	1.3507738631086000	[6,6,6,6,6,6,6,6,6,6,6,6]	[]
72	1	1.3507738631085970	[8,8,8,8,8,8,8,8,8]	[]
72	1	1.3507719820709130	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1]	[]
73	1	1.3505399782605000	[2,2,2...2,2,1]	[]
73	1	1.3505393876910110	[1,1,1...1,1]	[]
73	1	1.3505393873737040	[1,1,1...1,1]	[]
73	1	1.3505377935703900	[2,2,2...2,2,1]	[]
74	1	1.3503127126005210	[2,2,2...2,2]	[]
74	1	1.3503125671925580	[1,1,1...1,1]	[]
74	1	1.3503125599985400	[2,2,2...2,2,1,1]	[]
74	1	1.3503123230713010	[2,2,2...2,2]	[]
74	1	1.3503122853578950	[2,2,2...2,2]	[]
75	1	1.3500925079004050	[6,6,6,6,6,6,6,6,6,6,6,6,3]	[]
76	1	1.3498772953394710	[2,2,2...2,2]	[]
76	1	1.3498763752790660	[4,4,4...4,4,2,2]	[]
76	1	1.3498763161816630	[2,2,2...2,2]	[]
76	1	1.3498759223293810	[2,2,2...2,2,1,1]	[]
76	1	1.3498758069705090	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1,1,1]	[]
76	1	1.3498753401950570	[3,3,3...3,3,1]	[]
77	1	1.3496685473976890	[10,10,10,10,10,10,10,5,2]	[]
77	1	1.3496666860967510	[8,8,8,8,4,4,4,4,4,4,4,4,4,4,4,1]	[]
77	1	1.3496650418609910	[8,8,8,8,4,4,4,4,4,4,4,4,4,4,4,1]	[]
78	1	1.3494642266654190	[6,6,6,6,6,6,6,6,6,6,6,6,6]	[]
78	1	1.3494641646445620	[16,16,12,8,8,8,6,4]	[]
78	1	1.3494635955910530	[4,4,4...4,4,2,2,2,2,2,2,2,2,2,2,2,2,2]	[]
78	1	1.3494624028243750	[4,4,4...4,4,2,2,2,2,2,2,2,2,2,2,2]	[]
79	1	1.3492646224923330	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1,1]	[]
79	1	1.3492643703750250	[4,4,4...4,4,2,2,2,2,2,2,2,2,2,2,2,1]	[]
79	1	1.3492624615970880	[4,4,4...4,4,2,2,2,2,2,2,2,2,2,1]	[]
80	1	1.3490704161876030	[16,16,8,8,8,8,8,8]	[]
80	1	1.3490695658997720	[2,2,2...2,2]	[]
80	1	1.3490692517194350	[16,16,8,8,8,8,8,4,4]	[]
80	1	1.3490686060410360	[2,2,2...2,2]	[]
80	1	1.3490676745282360	[2,2,2...2,2,1,1]	[]
81	1	1.3488798341333860	[2,2,2...2,2,1]	[]
81	1	1.3488791049901470	[1,1,1...1,1]	[]
81	1	1.3488791024876710	[1,1,1...1,1]	[]
82	1	1.3486945666665880	[4,4,4...4,4,2]	[]
82	3	1.3486944304290120	[4,4,4...4,4,2]	[]
82	4	1.3486943528114230	[2,2,2...2,2]	[]
82	8	1.3486942351536500	[2,2,2...2,2]	[]
82	11	1.3486942251271020	[10,10,10,10,10,10,10,10,2]	[]
82	29	1.3486938440989410	[2,2,2...2,2]	[]
83	1	1.3485139228335830	[2,2,2...2,2,1]	[]
83	3	1.3485138068807920	[2,2,2...2,2,1]	[]
83	5	1.3485137099890310	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1,1]	[]
83	1	1.3485134454769150	[6,6,6,6,6,6,6,6,6,6,6,6,6,3,2]	[]
83	1	1.3485134347294180	[2,2,2...2,2,1]	[]
83	1	1.3485132974074370	[2,2,2...2,2,1]	[]
83	1	1.3485131103851840	[1,1,1...1,1]	[]
83	1	1.3485130252999250	[1,1,1...1,1]	[]
83	1	1.3485130146599070	[2,2,2...2,2,1,1,1,1,1,1,1,1,1]	[]
83	1	1.3485129817273100	[1,1,1...1,1]	[]
83	1	1.3485129711543390	[1,1,1...1,1]	[]
84	1	1.3483374602936810	[2,2,2...2,2,1,1]	[]
84	1	1.3483374566927910	[6,6,6,6,6,6,6,6,6,6,6,6,6,6]	[]
84	1	1.3483373360352030	[4,4,4...4,4]	[]
84	1	1.3483372694373580	[1,1,1...1,1]	[]
84	1	1.3483371442393710	[1,1,1...1,1]	[]
84	1	1.3483371274270900	[2,2,2...2,2]	[]
84	1	1.3483370990063010	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1]	[]
84	1	1.3483366575565800	[4,4,4...4,4]	[]
85	1	1.3481650432899750	[2,2,2...2,2,1]	[]
85	2	1.3481648799150190	[2,2,2...2,2,1]	[]
85	3	1.3481648462656760	[2,2,2...2,2,1]	[]
85	4	1.3481648017806690	[2,2,2...2,2,1]	[]
85	6	1.3481645786049940	[1,1,1...1,1]	[]
85	8	1.3481645097054200	[2,2,2...2,2,1]	[]
86	1	1.3479965780557490	[6,6,6,6,6,6,6,6,6,6,6,6,6,6,2]	[]
86	2	1.3479965621091900	[2,2,2...2,2]	[]
86	3	1.3479965515349540	[4,4,4...4,4,2]	[]
86	4	1.3479965309090270	[8,8,8,8,8,8,8,8,8,8,4,2]	[]
86	6	1.3479965140065030	[2,2,2...2,2]	[]
86	9	1.3479964976076290	[2,2,2...2,2]	[]
86	10	1.3479964882883210	[2,2,2...2,2]	[]
86	13	1.3479963394464080	[1,1,1...1,1]	[]
86	14	1.3479962858130920	[1,1,1...1,1]	[]
86	17	1.3479959966442870	[1,1,1...1,1]	[]
86	18	1.3479959848116340	[1,1,1...1,1]	[]
86	20	1.3479959430730140	[1,1,1...1,1]	[]
86	23	1.3479957088904670	[2,2,2...2,2]	[]
87	1	1.3478320068265330	[2,2,2...2,2,1]	[]
87	2	1.3478319657797090	[1,1,1...1,1]	[]
87	3	1.3478319651890900	[1,1,1...1,1]	[]
87	6	1.3478318753486540	[1,1,1...1,1]	[]
87	8	1.3478318490612010	[2,2,2...2,2,1]	[]
87	12	1.3478318124202300	[2,2,2...2,2,1]	[]
87	13	1.3478318075365380	[2,2,2...2,2,1,1,1,1,1,1,1,1,1]	[]
87	16	1.3478317385147460	[2,2,2...2,2,1]	[]
87	19	1.3478316881598230	[6,6,6,6,6,6,6,6,6,6,6,6,6,6,3]	[]
87	23	1.3478315682652710	[1,1,1...1,1]	[]
87	27	1.3478315049570140	[2,2,2...2,2,1]	[]
87	38	1.3478313494733330	[4,4,4...4,4,2,2,2,2,2,2,2,2,2,1]	[]
87	41	1.3478313372235720	[6,6,6,6,6,6,6,6,6,6,6,6,6,6,3]	[]
88	1	1.3476712955692840	[4,4,4...4,4]	[]
88	2	1.3476712752469050	[3,3,3...3,3,1]	[]
88	3	1.3476712740014230	[3,3,3...3,3,1]	[]
88	5	1.3476712642010130	[2,2,2...2,2]	[]
88	8	1.3476709444097590	[4,4,4...4,4]	[]
88	19	1.3476705597899510	[1,1,1...1,1]	[]
88	30	1.3476700239923210	[2,2,2...2,2]	[]
89	1	1.3475138807911930	[2,2,2...2,2,1]	[]
89	2	1.3475136207442450	[2,2,2...2,2,1]	[]
89	4	1.3475135501580690	[2,2,2...2,2,1]	[]
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91	1	1.3472087891606390	[2,2,2...2,2,1]	[]
92	1	1.3470620364267030	[4,4,4...4]	[]
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93	5	1.3469173378373860	[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,3]	[]
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93	10	1.3469172587656360	[1,1,1...1,1]	[]
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93	14	1.3469171881943020	[1,1,1...1,1]	[]
93	19	1.3469171387084430	[1,1,1...1,1]	[]
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93	41	1.3469169875224410	[1,1,1...1,1]	[]
93	50	1.3469168220652220	[1,1,1...1,1]	[]
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94	14	1.3467759996447840	[1,1,1...1,1]	[]
94	15	1.3467759820432080	[1,1,1...1,1]	[]
94	18	1.3467759459878180	[2,2,2...2,2]	[]
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94	25	1.3467758642926680	[2,2,2...2,2]	[]
94	30	1.3467758174063200	[1,1,1...1,1]	[]
94	39	1.3467757782947170	[3,3,3...3,1]	[]
94	45	1.3467757543664780	[1,1,1...1,1]	[]
94	49	1.3467757317822580	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1,1,1]	[]
94	90	1.3467755363389020	[1,1,1...1,1]	[]
94	93	1.3467755278399850	[1,1,1...1,1]	[]
94	99	1.3467755106054270	[1,1,1...1,1]	[]
94	108	1.3467754562115750	[1,1,1...1,1]	[]
95	1	1.3466382350737020	[2,2,2...2,2,1]	[]
95	3	1.3466380444634900	[2,2,2...2,2,1]	[]
95	4	1.3466380400470320	[2,2,2...2,2,1]	[]
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95	60	1.3466373871435980	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1,1,1,1]	[]
95	72	1.3466372001102030	[2,2,2...2,2,1]	[]
96	0	1.3465029252118600	[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]	[]
96	2	1.3465027555318980	[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6]	[]
96	0	1.3465026159284220	[8,8,8,8,8,8,8,8,8,8,4,4,4,4]	[]
96	0	1.3465025471662060	[2,2,2...2,2]	[]
96	0	1.3465025414156340	[2,2,2...2,2]	[]
96	0	1.3465024563681990	[3,3,3...3]	[]
96	0	1.3465023849640030	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1,1,1]	[]
96	0	1.3465021022179490	[1,1,1...1,1]	[]
96	0	1.3465020649066430	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1]	[]
96	0	1.3465020447086510	[2,2,2...2,2]	[]
96	0	1.3465020005760570	[1,1,1...1,1]	[]
96	0	1.3465019913397740	[1,1,1...1,1]	[]
96	0	1.3465019586497800	[2,2,2...2,2,1,1,1,1,1,1,1,1,1,1,1,1]	[]
96	0	1.3465018803000710	[1,1,1...1,1]	[]

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