Table for CAN(5,k,15) for k up to 10000

Last Updated Sun May 8 14:02:10 MST 2016

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;5,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 6 759375 Derive from strength 6 7 860625 Ji-Li-Yin 17 1048574 orthogonal array fuse 18 1419853 orthogonal array fuse fuse 19 2278123 Add 1 factors 20 2476091 orthogonal array fuse fuse fuse fuse 24 3145719 perfect hash family3,24,17 25 4000318 Martirosyan-TVT variant 26 4002326 Martirosyan-TVT 27 4004850 Martirosyan-TVT variant 28 4007360 Martirosyan-TVT 29 4008492 Martirosyan-TVT variant 30 4017134 Martirosyan-TVT 31 4017834 Martirosyan-TVT variant 32 4018338 Martirosyan-TVT 33 4022118 Martirosyan-TVT variant 34 4025898 Martirosyan-TVT 35 4648897 Martirosyan-TVT variant 36 4673419 Martirosyan-TVT 37 6281389 Add 1 factors 39 6291438 perfect hash family6,39,17 48 7340011 perfect hash family7,48,17 55 8388584 perfect hash family8,55,17 71 9437157 perfect hash family9,71,17 88 10485730 perfect hash family10,88,17 102 11245104 Power CT17^2T11 119 11346354 Power CT17^2T10 289 11534303 Power CT17^2 290 13596713 Add 1 factors 291 15105563 Add 2 factors 292 15814313 Add 3 factors 293 16677386 Add 4 factors 294 16771886 Add 5 factors 295 17631503 Add 16 factors 305 17635343 Add 16 factors 306 18935967 Add 17 factors 307 20206410 Power N-CT19^2Arc(3) 324 21064680 Power N-CT19^2T1T1 342 21922950 Power N-CT19^2T1 361 22781220 Power N-CT19^2 379 23725729 Martirosyan-TVT variant 449 23742107 Martirosyan-TVT variant 512 23758485 Martirosyan-TVT 544 23866005 Martirosyan-TVT 545 23925953 Martirosyan-TVT variant 546 23942331 Martirosyan-TVT 547 24722427 Martirosyan-TVT variant 557 25502523 Martirosyan-TVT variant 578 25522165 Martirosyan-TVT 580 27895641 Martirosyan-TVT 581 29404491 Martirosyan-TVT variant 582 29424133 Martirosyan-TVT 584 30132883 Martirosyan-TVT 586 30995956 Martirosyan-TVT 588 31090456 Martirosyan-TVT 590 31950073 Martirosyan-TVT 610 31953913 Martirosyan-TVT 612 33254537 Martirosyan-TVT 614 34836088 Martirosyan-TVT 615 37091638 Martirosyan-TVT variant 620 38636587 Power N-CT31^2T11 648 38845414 Martirosyan-TVT 649 39219873 Power N-CT29^2Arc(2)T5 672 39221005 Power N-CT29^2T5T1 696 39222137 Power N-CT29^2T5 697 39304815 Power N-CT31^2Arc(2)T7 720 39305515 Power N-CT31^2T7T1 744 39306215 Power N-CT31^2T7 754 40078744 Power N-CT29^2T3 756 40080136 Power N-CT29^2T2T1 783 40081268 Power N-CT29^2T2 784 40082646 Power N-CT29^2T1T1 812 40083778 Power N-CT29^2T1 841 40084910 Power N-CT29^2 842 40167588 Power N-CT31^2Arc(2)T2 868 40167856 Power N-CT31^2T3 870 40168288 Power N-CT31^2T2T1 899 40168988 Power N-CT31^2T2 900 40176930 Power N-CT31^2T1T1 930 40177630 Power N-CT31^2T1 961 40178330 Power N-CT31^2 962 40183370 Power N-CT31^2+1 963 40221170 Power N-CT31^2+2 964 40258970 Power N-CT31^2+3 965 44042330 Add 1 factors 992 44201203 Power CT32^2T1 1024 44201707 Power CT32^2 1025 44243287 Power CT32^2+1 1026 44284867 Power CT32^2+2 1044 46734180 Power N-CT37^2Arc(10) 1072 48342150 Power N-CT37^2Arc(9) 1073 49307161 Martirosyan-TVT variant 1088 49336895 Martirosyan-TVT 1089 49465485 Martirosyan-TVT variant 1090 49533703 Martirosyan-TVT 1092 49550081 Martirosyan-TVT 1101 49950120 Power N-CT37^2Arc(8) 1131 51558090 Power N-CT37^2Arc(7) 1162 53166060 Power N-CT37^2Arc(6) 1194 54774030 Power N-CT37^2Arc(5) 1227 56382000 Power N-CT37^2Arc(4) 1235 57671515 perfect hash family55,1235,17 1261 57989970 Power N-CT37^2Arc(3) 1734 59479444 Power CT23^3T17T6T6 2023 59580694 Power CT23^3T16T6T6 4913 59768643 Power CT23^3T6T6T6 5202 60139922 Power CT23^3T6T6T5 5508 60511201 Power CT23^3T6T5T5 5832 60882480 Power CT23^3T5T5T5 6120 61567439 Power CT23^3T6T5T3 6156 61740750 Power CT23^3T5T5T4 6647 61865788 Power CT23^3T6T6 7038 62237067 Power CT23^3T6T5 7452 62608346 Power CT23^3T5T5 7820 63293305 Power CT23^3T6T3 7866 63466616 Power CT23^3T5T4 8280 63664584 Power CT23^3T5T3 8993 63962933 Power CT23^3T6 9522 64334212 Power CT23^3T5 10000 65192482 Power CT23^3T4

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