Table for CAN(6,k,17) 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,17) 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 18 24137569 orthogonal array 19 46855281 extend by one factor 20 47045879 fuse symbols 21 82492647 extend by one factor 24 96550273 perfect hash family 36 119267988 Martirosyan-Tran van Trung 37 186001828 extend by one factor 39 217238113 perfect hash family 40 226441584 Martirosyan-Tran van Trung 42 265513249 perfect hash family 44 313788385 perfect hash family 48 337925953 perfect hash family 86 362063521 perfect hash family 290 386201089 Power 18^2 291 495780369 extend by one factor 292 607875105 extend by one factor 294 699989473 perfect hash family 361 749684481 Power 19^2 362 752734049 Power 20^2 514 772402177 perfect hash family 515 964987153 extend by one factor 518 1086190561 perfect hash family 519 1278775537 extend by one factor 578 1288644212 Martirosyan-Tran van Trung 580 1299020468 Martirosyan-Tran van Trung 582 1470228420 Martirosyan-Tran van Trung 584 1643664884 Martirosyan-Tran van Trung 588 1735779252 Martirosyan-Tran van Trung 612 1785474260 Martirosyan-Tran van Trung 966 1789019806 linear hash family 1028 1908287793 Power 36^2 1029 2165099585 extend by one factor 1030 2421911377 extend by one factor 1031 2678723169 extend by one factor 1057 2703407617 perfect hash family 1369 2790027406 linear hash family 1370 3046839198 extend by one factor 1450 3089608705 perfect hash family 1451 3346420497 extend by one factor 1454 3403397089 perfect hash family 1729 3475809793 perfect hash family 10000 3697307598 Power 31^3

Graph: