Table for CAN(5,k,12) for k up to 10000

Last Updated Fri Sep 20 11:41:02 MST 2013

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,12) 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 248832 Derive from strength 6 7 296130 Derive from strength 6 8 323050 Add a symbol 9 352418 Add a symbol 14 371291 orthogonal array fuse 15 657203 AZ1 16 916979 Add 2 factors 17 1048568 orthogonal array fuse fuse fuse fuse 18 1113851 perfect hash family3,18,13,c fuse 19 1113870 perfect hash family3,19,14 20 1349906 Martirosyan-Tran van Trung 22 1354130 Martirosyan-Tran van Trung 24 1392745 Martirosyan-Tran van Trung 26 1395052 Martirosyan-Tran van Trung 28 1400737 Martirosyan-Tran van Trung 29 1926757 AZ1 31 2227740 perfect hash family6,31,14 34 2599030 perfect hash family7,34,14 36 2970251 perfect hash family8,36,13,c fuse 42 2970320 perfect hash family8,42,14 43 3341531 perfect hash family9,43,13,c fuse 48 3341610 perfect hash family9,48,14 52 3712811 perfect hash family10,52,13,c fuse 59 3712900 perfect hash family10,59,14 78 3961731 Power CT13^2T7 91 4009029 Power CT13^2T6 104 4035949 Power CT13^2T5 117 4065317 Power CT13^2T4 169 4084091 perfect hash family11,169,13,c fuse 170 4084190 Power CT13^2+1 171 4663802 AZ1 172 5151674 Add 2 factors 173 5379770 Add 3 factors 174 5930450 Add 4 factors 182 6052811 Add 13 factors 183 6052910 Add 13 factors 184 6632522 AZ1 185 7121978 Add 2 factors 186 7350074 Add 3 factors 187 7901198 Add 13 factors 190 7996754 Martirosyan-Tran van Trung 196 8005536 Martirosyan-Tran van Trung 204 8071683 Martirosyan-Tran van Trung 206 8080465 Martirosyan-Tran van Trung 208 8098029 Martirosyan-Tran van Trung 210 8147557 Martirosyan-Tran van Trung 224 8209031 Martirosyan-Tran van Trung 226 8215268 Martirosyan-Tran van Trung 234 8250396 Martirosyan-Tran van Trung 252 8271765 Martirosyan-Tran van Trung 260 8275307 Martirosyan-Tran van Trung 280 8276638 Martirosyan-Tran van Trung 338 8285420 Martirosyan-Tran van Trung 340 8328863 Martirosyan-Tran van Trung 342 8908475 Martirosyan-Tran van Trung 344 9396347 Martirosyan-Tran van Trung 346 9624443 Martirosyan-Tran van Trung 348 10175123 Martirosyan-Tran van Trung 364 10297484 Martirosyan-Tran van Trung 366 10318494 Martirosyan-Tran van Trung 367 11272062 AZ1 368 11890996 Martirosyan-Tran van Trung 369 12130590 Add 3 factors 370 12606408 Martirosyan-Tran van Trung 372 12834504 Martirosyan-Tran van Trung 374 12870392 Add 13 factors 377 12890672 Add 13 factors 379 12911682 Add 13 factors 380 13480740 Martirosyan-Tran van Trung 392 13489522 Martirosyan-Tran van Trung 400 13571335 Power N-CT23^2Arc(2)T4 418 13609950 Power N-CT23^2T4T1 437 13648565 Power N-CT23^2T4 443 13772980 Power N-CT23^2Arc(4) 463 13811595 Power N-CT23^2Arc(3) 484 13850210 Power N-CT23^2T1T1 506 13888825 Power N-CT23^2T1 530 13927440 Power N-CT23^2+1 532 13950510 Power N-CT23^2+3 553 14001675 Power N-CT29^2T3S9 596 14007360 Power N-CT29^2Arc(10) 616 14533380 Power N-CT29^2Arc(9) 637 15059400 Power N-CT29^2Arc(8) 651 15391041 Power CT27^2Arc(3) 676 15396726 Power CT27^2T1T1 702 15402411 Power CT27^2T1 730 15408096 Power CT27^2+1 731 16607184 AZ1 732 17285136 Add 2 factors 733 17513232 Add 3 factors 757 17689500 Power N-CT29^2Arc(3) 784 18215520 Power N-CT29^2T1T1 812 18741540 Power N-CT29^2T1 841 19267560 Power N-CT29^2 842 20505060 AZ1 843 21189348 Add 2 factors 844 21417444 Add 3 factors 868 21450387 Power N-CT31^2T3 899 21976407 Power N-CT31^2T2 961 22277390 Power N-CT31^2 968 22726791 Martirosyan-Tran van Trung 1012 22765406 Martirosyan-Tran van Trung 1014 22804021 Martirosyan-Tran van Trung 1026 22838583 Martirosyan-Tran van Trung 1060 22846239 Martirosyan-Tran van Trung 1064 22869309 Martirosyan-Tran van Trung 1092 22920474 Martirosyan-Tran van Trung 1098 22954783 Martirosyan-Tran van Trung 1106 22967037 Martirosyan-Tran van Trung 1176 22972722 Martirosyan-Tran van Trung 1192 23062845 Martirosyan-Tran van Trung 1194 24016413 Martirosyan-Tran van Trung 1204 24109136 Martirosyan-Tran van Trung 1228 24220016 Martirosyan-Tran van Trung 1600 24505140 perfect hash family66,1600,14 1601 25849032 AZ1 1764 26164389 Power CT23^3T14T9T9 2744 26183262 Power CT23^3T9T9T9 2940 26469174 Power CT23^3T9T9T8 3136 26728950 Power CT23^3T9T9T7 3150 26755086 Power CT23^3T9T8T8 3332 26860539 Power CT23^3T9T9T6 3528 26925822 Power CT23^3T9T9T5 3724 26925841 Power CT23^3T9T9T4 3920 27161877 Power CT23^3T9T9T3 4312 27166101 Power CT23^3T9T9T1 4508 27204716 Power CT23^3T9T9 4704 27246242 Power CT25^3T11T11T1 4900 27248549 Power CT25^3T11T11 5096 27350879 Power CT27^3T13T13T1 5292 27356564 Power CT27^3T13T13 5460 27636791 Power CT27^3T13T12T1 5670 27642476 Power CT27^3T13T12 5824 27896567 Power CT27^3T13T11T1 6048 27902252 Power CT27^3T13T11 6075 27928388 Power CT27^3T12T12 6118 27947295 Power CT23^3T9T4 6384 27988821 Power CT25^3T11T6T1 6650 27991128 Power CT25^3T11T6 6916 28093458 Power CT27^3T13T8T1 7182 28099143 Power CT27^3T13T8 7406 28226170 Power CT23^3T9 7700 28231388 Power CT25^3T11T3 7742 28265389 Power CT25^3T11S3 8064 28267696 Power CT25^3T11T1T1 8400 28270003 Power CT25^3T11T1 8750 28272310 Power CT25^3T11 8778 28363270 Power CT27^3T13S4 9114 28368955 Power CT27^3T13S3 9464 28374640 Power CT27^3T13T1T1 9828 28380325 Power CT27^3T13T1 10000 28386010 Power CT27^3T13

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