Table for CAN(6,k,22) for k up to 10000

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,22) 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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k N Source 7 113379904 composition 24 148035888 fuse symbols 26 244140622 fuse symbols 28 387420484 fuse symbols 31 592143549 perfect hash family 48 725577975 Martirosyan-Tran van Trung 49 1082459577 extend by one factor 50 1105668677 Martirosyan-Tran van Trung 52 1175980637 Martirosyan-Tran van Trung 53 1617554231 extend by one factor 54 1734240579 Martirosyan-Tran van Trung 56 1735303451 Martirosyan-Tran van Trung 57 1776430645 perfect hash family 62 1924466532 perfect hash family 115 2220538306 perfect hash family 530 2368574193 Power 24^2 531 2998142517 extend by one factor 532 3638464353 extend by one factor 626 3906249937 Power 26^2 627 4760627461 extend by one factor 628 5615004985 extend by one factor 730 6198727729 Power 28^2 731 7242296101 extend by one factor 735 7253758464 perfect hash family 744 7697866125 perfect hash family 1058 7783436425 Martirosyan-Tran van Trung 1060 7831384985 Martirosyan-Tran van Trung 1062 8804801891 Martirosyan-Tran van Trung 1064 9784939847 Martirosyan-Tran van Trung 1104 10052725431 Martirosyan-Tran van Trung 2210 10158091637 linear hash family 2211 11642808101 extend by one factor 2212 13127524565 extend by one factor 2213 14612241029 extend by one factor 2214 16096957493 extend by one factor 2401 17319353217 Power 49^2 2402 17690698817 Power 50^2 4805 17764306441 perfect hash family 6477 18208414102 perfect hash family 10000 18356449989 perfect hash family

Graph: