Table for CAN(6,k,15) 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,15) 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 11390625 composition 17 16777215 fuse symbols 18 24137567 fuse symbols 19 37899917 extend by one factor 20 47045877 fuse symbols 23 67108857 perfect hash family 34 81378811 Martirosyan-Tran van Trung 36 103371063 Martirosyan-Tran van Trung 37 143767083 extend by one factor 39 167772141 perfect hash family 41 184549355 perfect hash family 42 218103783 perfect hash family 43 234880997 perfect hash family 85 251658211 perfect hash family 289 268435425 Power 17^2 290 340863165 extend by one factor 291 425464395 extend by one factor 292 486539207 perfect hash family 513 536870849 perfect hash family 514 649911959 extend by one factor 516 754974631 perfect hash family 517 868822141 extend by one factor 544 882026771 Martirosyan-Tran van Trung 576 918027919 Martirosyan-Tran van Trung 578 1005147717 Martirosyan-Tran van Trung 580 1122632545 Martirosyan-Tran van Trung 964 1220682151 linear hash family 1026 1302060961 Power 34^2 1027 1457050411 extend by one factor 1028 1612039861 extend by one factor 1029 1767029311 extend by one factor 1056 1879047969 perfect hash family 1057 2034037419 extend by one factor 1059 2097151751 perfect hash family 1425 2147483393 perfect hash family 1426 2302472843 extend by one factor 1428 2365587175 perfect hash family 1728 2415918817 perfect hash family 10000 2522743111 Power 31^3

Graph: