Table for CAN(6,k,16) for k up to 10000

Last Updated Tue Nov 21 02:19:04 MST 2017

Locate the k in the first column that is at least as large as the number of factors in which you are interested. Then let N be the number of rows (tests) given in the second column. A CA(N;6,k,16) exists according to a construction in the reference (cryptically) given in the third column. The accompanying graph plots N vertically against log k (base 10).

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kNSource
1716777216orthogonal array
1824137567orthogonal array fuse
1939866207Add 1 factors
2047045875orthogonal array fuse fuse fuse
22492830565-Restricted SCPHF RE (CL)
24502660964-Restricted SCPHF RE (CL)
25503275363-Restricted SCPHF RE (CL)
2650331616SCPHF Random Extension (CLS)
33650116965-Restricted SCPHF RE (CL)
35660602565-Restricted SCPHF RE (CL)
36670432964-Restricted SCPHF RE (CL)
37671047363-Restricted SCPHF RE (CL)
39671085762-Restricted SCPHF RE (CL)
4067108816SCPHF Random Extension (CLS)
4167108861CPHF Random Extension (CLS)
51817888965-Restricted SCPHF RE (CL)
56828374565-Restricted SCPHF RE (CL)
58838204964-Restricted SCPHF RE (CL)
61838819363-Restricted SCPHF RE (CL)
63838857762-Restricted SCPHF RE (CL)
6683886016SCPHF Random Extension (CLS)
73975175365-Restricted SCPHF RE (CL)
82985660965-Restricted SCPHF RE (CL)
89996146565-Restricted SCPHF RE (CL)
981005976964-Restricted SCPHF RE (CL)
1031006591363-Restricted SCPHF RE (CL)
1041006629762-Restricted SCPHF RE (CL)
1131142947365-Restricted SCPHF RE (CL)
1271153432965-Restricted SCPHF RE (CL)
1411163918565-Restricted SCPHF RE (CL)
1501173748964-Restricted SCPHF RE (CL)
1531174363363-Restricted SCPHF RE (CL)
163117440416SCPHF Random Extension (CLS)
164117440506CPHF Random Extension (CLS)
236134217616SCPHF Random Extension (CLS)
268193100431SCPHF Random Extension (CLS) fuse
289268435440Power CT17^2
290346084080Add 1 factors
291383804400Add 2 factors
292414278640Add 3 factors
293430007280Add 4 factors
305445735920Add 16 factors
306484947440Add 17 factors
314536453584Martirosyan-TVT
315536572624Martirosyan-TVT variant
316536691664Martirosyan-TVT
317536713984Martirosyan-TVT variant
318536736304Martirosyan-TVT
512536870416perfect hash family32,512,16,c
513536870880perfect hash family32,513,17
514630244320Add 1 factors
530671088075perfect hash family5,530,236
536688559824Martirosyan-TVT
544763894833Martirosyan-TVT
545764251953Martirosyan-TVT variant
546764609073Martirosyan-TVT
547777976785Martirosyan-TVT variant
558794007921Martirosyan-TVT
577794990721Martirosyan-TVT variant
578804049729Martirosyan-TVT
600805179120Power CT25^2T1
625805240560Power CT25^2
639805305690perfect hash family6,639,236
641864188505perfect hash family6,651,237S5
648889192065Power N-CT41^2Trin1,2,24
663889192110Power N-CT41^2T24T2
664889192305Power N-CT41^2Arc(2)T24
680889192350Power N-CT41^2T24T1
697889192395Power N-CT41^2T24
702896552461Power N-CT41^2T23T2
703896552656Power N-CT41^2Arc(2)T23
720896552701Power N-CT41^2T23T1
738896552746Power N-CT41^2T23
741912281101Power N-CT41^2T22T2
742912281296Power N-CT41^2Arc(2)T22
760912281341Power N-CT41^2T22T1
779912281386Power N-CT41^2T22
780919460769Power N-CT41^2T21T2
781919460964Power N-CT41^2Arc(2)T21
800919461009Power N-CT41^2T21T1
820919461054Power N-CT41^2T21
825920645550Power N-CT41^2T16T8
840920649585Power N-CT41^2Trin1,8,15
858920649630Power N-CT41^2T15T8
875921694110Power N-CT41^2T16T6
890921698145Power N-CT41^2Trin1,6,15
910921698190Power N-CT41^2T15T6
914922680945Power N-CT41^2Trin1,2,17
936922680990Power N-CT41^2T17T2
937922681185Power N-CT41^2Arc(2)T17
960922681230Power N-CT41^2T17T1
984922681275Power N-CT41^2T17
1000922742670Power N-CT41^2T16T1
1025922742715Power N-CT41^2T16
1040922746750Power N-CT41^2T15T1
1066922746795Power N-CT41^2T15
1089935329710Power N-CT41^2T8T8
1101936377985Power N-CT41^2Trin2,6,8
1128936378225Power N-CT41^2Trin1,6,8
1155936378270Power N-CT41^2T8T6
1160937361265Power N-CT41^2Trin1,5,8
1188937361310Power N-CT41^2T8T5
1192937422705Power N-CT41^2Trin1,4,8
1221937422750Power N-CT41^2T8T4
1225937426305Power N-CT41^2Trin2,2,8
1256937426545Power N-CT41^2Trin1,2,8
1287937426590Power N-CT41^2T8T2
1288937426785Power N-CT41^2Arc(2)T8
1320937426830Power N-CT41^2T8T1
1353937426875Power N-CT41^2T8
1365938475150Power N-CT41^2T6T2
1366938475345Power N-CT41^2Arc(2)T6
1400938475390Power N-CT41^2T6T1
1435938475435Power N-CT41^2T6
1440939458430Power N-CT41^2T5T1
1476939458475Power N-CT41^2T5
1480939519870Power N-CT41^2T4T1
1517939519915Power N-CT41^2T4
1521939523470Power N-CT41^2T2T2
1522939523665Power N-CT41^2Arc(2)T2
1560939523710Power N-CT41^2T2T1
1599939523755Power N-CT41^2T2
1600939523950Power N-CT41^2T1T1
1640939523995Power N-CT41^2T1
1681939524040Power N-CT41^2
16821065326280Add 1 factors
16921130298930Power N-CT47^2T11
17391130360370Power N-CT47^2T10
18331130364210Power N-CT47^2T8
18801130364450Power N-CT47^2T7
19271130364495Power N-CT47^2T6
19641141898610Power N-CT53^2Trin2,2,13
20131141898655Power N-CT53^2Trin2,2,12
20401142947170Power N-CT53^2T13T2
20911142947215Power N-CT53^2T12T2
21201143995730Power N-CT53^2T13
21731143995775Power N-CT53^2T12
22131145044530perfect hash family14,2213,51
22581156468095Power N-CT59^2Trin1,3,18
22961156529535Power N-CT59^2T18T3
25031156578690Power N-CT53^2Trin2,2,2
26011157627250Power N-CT53^2T2T2
27031158675810Power N-CT53^2T2
28121159724370Power N-CT53^2+3
28561171209570Power N-CT59^2T8T3
29771171213650Power N-CT59^2Trin3,3,3
30831172196690Power N-CT59^2Trin1,3,3
31111172254050Power N-CT61^2T10
31361172258130Power N-CT59^2T3T3
31391173118290Power N-CT59^2Arc(3)T3
31931173179730Power N-CT59^2Arc(2)T3
32481173241170Power N-CT59^2T3T1
34161173302610Power N-CT61^2T5
35381174285650Power N-CT61^2T3
37211174347090Power N-CT61^2
37231174400850Power N-CT61^2+2
37261174404210perfect hash family14,3726,66
37511201667250Power N-CT67^2Arc(12)
38071215298770Power N-CT67^2Arc(11)
39431226833395Power N-CT73^2Trin7,7,7
40261240460835Power N-CT73^2T12T7
41581240464675Power N-CT73^2T10T7
43561240464915Power N-CT73^2T7T7
44531254092355Power N-CT73^2T12
45991254096195Power N-CT73^2T10
48181254096435Power N-CT73^2T7
48191266675075Power N-CT79^2T18
49771266678915Power N-CT79^2T16
52141266679155Power N-CT79^2T13
53291267727955Power N-CT73^2
53471277164755Power N-CT83^2Arc(2)T17
54121278213315Power N-CT83^2T17T1
54291279257795Power N-CT89^2T28
56071279261635Power N-CT89^2T26
58741279261875Power N-CT89^2T23
62441281359235Power N-CT79^2+3
62531286602035Power N-CT83^2Arc(8)
63291287650595Power N-CT83^2Arc(7)
64061288699155Power N-CT83^2Arc(6)
64841289747715Power N-CT83^2Arc(5)
65631290796275Power N-CT83^2Arc(4)
67981291795635perfect hash family13,10609,103T37
72981293941955Power N-CT89^2T7
79211294990515Power N-CT89^2
79541305738435Power N-CT97^2T15
80361306414275Power N-CT101^2T19T3
84461306475715perfect hash family13,10609,103T21
86331306786995Power N-CT97^2T8
87221307462835Power N-CT101^2T12T3
91671307524275perfect hash family13,10609,103T14
94101307770035Power N-CT97^2+1
96041308445875Power N-CT101^2T3T3
100001308507315perfect hash family13,10609,103T5
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