Table for CAN(6,k,18) 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,18) 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 34012224 composition 8 45172485 composition 20 47045880 fuse symbols 21 86923800 extend by one factor 22 126801720 extend by one factor 24 148035884 fuse symbols 25 188183517 perfect hash family 40 229467115 Martirosyan-Tran van Trung 41 338538673 extend by one factor 42 447610231 extend by one factor 43 517504670 perfect hash family 45 611596428 perfect hash family 50 658642307 perfect hash family 95 705688186 perfect hash family 362 752734065 Power 20^2 363 945828021 extend by one factor 364 1146875529 extend by one factor 365 1347923037 extend by one factor 366 1364330492 perfect hash family 515 1505468129 perfect hash family 516 1835360915 extend by one factor 520 2117064556 perfect hash family 530 2368574129 Power 24^2 722 2448724477 Martirosyan-Tran van Trung 724 2485009309 Martirosyan-Tran van Trung 726 2781378571 Martirosyan-Tran van Trung 728 3085701385 Martirosyan-Tran van Trung 730 3292846827 Martirosyan-Tran van Trung 732 3309254282 Martirosyan-Tran van Trung 1372 3442006711 linear hash family 1373 3895689655 extend by one factor 1374 4349372599 extend by one factor 1681 4739541409 linear hash family 1682 5193224353 extend by one factor 1683 5646907297 extend by one factor 1805 6021872513 perfect hash family 1806 6475555457 extend by one factor 1810 6586423061 perfect hash family 1830 6633468940 perfect hash family 2415 6774606577 perfect hash family 10000 7113480535 Power 31^3

Graph: