Table for CAN(6,k,21) 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,21) 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 85766121 composition 24 148035887 fuse symbols 26 244140621 fuse symbols 28 387420483 fuse symbols 31 592143545 perfect hash family 48 717972548 Martirosyan-Tran van Trung 49 1020097868 extend by one factor 50 1094277022 Martirosyan-Tran van Trung 52 1095058264 Martirosyan-Tran van Trung 53 1472725624 extend by one factor 54 1709277444 Martirosyan-Tran van Trung 56 1710340314 Martirosyan-Tran van Trung 57 1776430633 perfect hash family 62 1924466519 perfect hash family 115 2220538291 perfect hash family 530 2368574177 Power 24^2 531 2940908597 extend by one factor 532 3523018937 extend by one factor 626 3906249921 Power 26^2 627 4682956341 extend by one factor 628 5459662761 extend by one factor 730 6198727713 Power 28^2 731 7147425813 extend by one factor 735 7253758415 perfect hash family 744 7697866073 perfect hash family 1058 7710752772 Martirosyan-Tran van Trung 1060 7758561676 Martirosyan-Tran van Trung 1062 8628583696 Martirosyan-Tran van Trung 1064 9508381636 Martirosyan-Tran van Trung 1104 9914604540 Martirosyan-Tran van Trung 2210 10051615659 linear hash family 2211 11401357479 extend by one factor 2212 12751099299 extend by one factor 2213 14100841119 extend by one factor 2214 15330815683 linear hash family 2401 16321565873 Power 49^2 2402 17508432337 Power 50^2 2404 17520932209 Power 52^2 4805 17764306321 perfect hash family 6477 18208413979 perfect hash family 10000 18356449865 perfect hash family

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