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

Last Updated Tue Jan 31 05:20:10 MST 2012

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 a factor
2047045875orthogonal array fuse fuse fuse
2167108816perfect hash family4,21,16,c
2367108860perfect hash family4,23,17
3279691776double OA (Colbourn-Zhou)
3480736256double OA (Colbourn-Zhou)
36109985476Martirosyan-Tran van Trung
37157912756Add a factor
39167772150perfect hash family10,39,17
40184549216perfect hash family11,40,16,c
44184549365perfect hash family11,44,17
50201326580perfect hash family12,50,17
53218103795perfect hash family13,53,17
60234881010perfect hash family14,60,17
80251658016perfect hash family15,80,16,c
85251658225Power CT17^2Tlev
256268435216perfect hash family16,256,16,c
289268435440Power CT17^2
290359443200Add a factor
291456061200Add a factor
292469762020perfect hash family28,292,17
293520093665perfect hash family31,293,17
512536870416perfect hash family32,512,16,c
513536870880perfect hash family32,513,17
514662392800Add a factor
516754974675perfect hash family45,516,17
517880496595Add a factor
518905969610perfect hash family54,518,17
544938450763Martirosyan-Tran van Trung
576967090799Martirosyan-Tran van Trung
578971984881perfect hash familyD16,578,34^11 17^5
5791130421361Add a factor
5891155551056Power N-CT31^2T12
6201162730724Power N-CT31^2T11
6511182793665Power N-CT31^2T10
7131182793709Power N-CT31^2T8
9621195376625Power N-CT31^2+1
9641211043825Power N-CT31^2+3
10241275068400Power CT32^2
10261291780080Power CT32^2+2
10271468788720Add a factor
10281645797360Add a factor
10291822806000Add a factor
10561879048080perfect hash family112,1056,17
10721937345805Power N-CT37^2Arc(9)
11011985273085Power N-CT37^2Arc(8)
11312033200365Power N-CT37^2Arc(7)
11622081127645Power N-CT37^2Arc(6)
11942129054925Power N-CT37^2Arc(5)
14252147483520perfect hash family128,1425,17
49132281701345Power CT31^3T14T14T14
52022289061696Power CT31^3T14T14T13
55082296422047Power CT31^3T14T13T13
58322303782398Power CT31^3T13T13T13
61202319330355Power CT31^3T14T13T11
61562319511038Power CT31^3T13T13T12
64802326690706Power CT31^3T13T13T11
66472332032989Power CT31^3T14T14T8
70382339393340Power CT31^3T14T13T8
92482344615905Power CT32^3T15T15
97922351976256Power CT32^3T15T14
100002359336607Power CT31^3T13T13
 Graph: