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

Last Updated Fri Mar 27 17:29:14 MST 2015

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 294080 Augment OA 8 318386 Augment OA 9 343426 Augment OA 10 366175 orthogonal array fuse postop NCK 11 368394 orthogonal array fuse postop NCK 12 370873 orthogonal array fuse postop NCK 13 371076 orthogonal array fuse postop NCK 14 371273 orthogonal array fuse postop NCK 15 632736 extended OA (Colbourn) special fuse 16 916697 Add 2 factors 17 1048568 orthogonal array fuse fuse fuse fuse 18 1113225 perfect hash family3,18,13 19 1113816 perfect hash family3,19,14 20 1344790 Martirosyan-TVT 21 1347141 Martirosyan-TVT variant 22 1351233 Martirosyan-TVT 23 1373631 Martirosyan-TVT variant 24 1391999 Martirosyan-TVT 25 1393197 Martirosyan-TVT variant 26 1394181 Martirosyan-TVT 27 1395395 Martirosyan-TVT variant 28 1400719 Martirosyan-TVT 29 1926739 Add 1 factors 31 2227632 perfect hash family6,31,14 32 2598707 perfect hash family7,34,14T1 34 2598904 perfect hash family7,34,14 36 2968600 perfect hash family8,36,13 37 2969782 perfect hash family8,42,14S2 39 2969979 perfect hash family8,42,14T1 42 2970176 perfect hash family8,42,14 43 3289576 Power N-CT9^2Arc(2)T3 46 3309050 Power N-CT9^2Arc(5) 48 3314616 Power N-CT9^2T3T1 51 3334090 Power N-CT9^2Arc(4) 54 3339656 Power N-CT9^2T3 57 3359130 Power N-CT9^2Arc(3) 64 3384170 Power N-CT9^2T1T1 72 3409210 Power N-CT9^2T1 81 3434250 Power N-CT9^2 82 3661740 Power N-CT9^2+1 83 3683930 Power N-CT9^2+2 84 3708720 Power N-CT9^2+3 88 4002315 Power CT11^2T3 91 4004829 Power CT13^2T6 99 4027355 Power CT11^2T2 104 4029135 Power CT13^2T5 110 4050104 Power CT11^2T1 121 4052323 Power CT11^2 130 4076924 Power CT13^2T3 132 4078940 Power CT13^2T2T1 143 4079143 Power CT13^2T2 144 4081419 Power CT13^2T1T1 156 4081622 Power CT13^2T1 169 4081825 Power CT13^2 170 4083992 Power CT13^2+1 171 4663604 Add 1 factors 172 5151476 Add 2 factors 173 5379572 Add 3 factors 174 5670578 Add 4 factors 175 5708693 Add 5 factors 182 6050545 Add 13 factors 183 6052712 Add 13 factors 184 6632324 Add 1 factors 185 7121780 Add 2 factors 186 7349876 Add 3 factors 187 7641025 Add 4 factors 188 7679140 Add 5 factors 191 7988148 Martirosyan-TVT variant 196 7996930 Martirosyan-TVT 197 8054284 Martirosyan-TVT variant 198 8063066 Martirosyan-TVT 205 8064846 Martirosyan-TVT variant 207 8073628 Martirosyan-TVT variant 208 8091192 Martirosyan-TVT 209 8114757 Martirosyan-TVT variant 211 8132321 Martirosyan-TVT variant 220 8193795 Martirosyan-TVT 224 8196014 Martirosyan-TVT 227 8202251 Martirosyan-TVT variant 234 8237379 Martirosyan-TVT 242 8239975 Martirosyan-TVT 252 8264576 Martirosyan-TVT 260 8268140 Martirosyan-TVT 264 8271487 Martirosyan-TVT 281 8271690 Martirosyan-TVT variant 286 8280472 Martirosyan-TVT 288 8282748 Martirosyan-TVT 312 8282951 Martirosyan-TVT 338 8283154 Martirosyan-TVT 339 8319597 Martirosyan-TVT variant 340 8328379 Martirosyan-TVT 342 8907991 Martirosyan-TVT 344 9395863 Martirosyan-TVT 346 9623959 Martirosyan-TVT 348 9914965 Martirosyan-TVT 350 9953080 Martirosyan-TVT 364 10294932 Martirosyan-TVT 366 10318296 Martirosyan-TVT 367 11271864 Add 1 factors 368 11888770 Martirosyan-TVT 369 12130392 Add 3 factors 370 12434268 Add 4 factors 371 12472383 Add 5 factors 372 12833862 Martirosyan-TVT 374 12867840 Add 13 factors 377 12888120 Add 13 factors 379 12911484 Add 13 factors 383 13409291 Power N-CT23^2Arc(3)T4 391 13411237 Power N-CT23^2T6 400 13431689 Power N-CT23^2Arc(2)T4 418 13454087 Power N-CT23^2T4T1 437 13476485 Power N-CT23^2T4 443 13646708 Power N-CT23^2Arc(4) 463 13669106 Power N-CT23^2Arc(3) 484 13691504 Power N-CT23^2T1T1 506 13713902 Power N-CT23^2T1 529 13736300 Power N-CT23^2 530 13919980 Power N-CT23^2+1 531 13931960 Power N-CT23^2+2 532 13941800 Power N-CT23^2+3 553 14000642 Power N-CT29^2T3S9 574 14001856 Power N-CT29^2T2S9 596 14007180 Power N-CT29^2Arc(10) 616 14533200 Power N-CT29^2Arc(9) 637 15059220 Power N-CT29^2Arc(8) 651 15345692 Power CT27^2Arc(3) 676 15346906 Power CT27^2T1T1 702 15348120 Power CT27^2T1 729 15349334 Power CT27^2 730 15407898 Power CT27^2+1 731 16606986 Add 1 factors 732 17284938 Add 2 factors 733 17513034 Add 3 factors 757 17689320 Power N-CT29^2Arc(3) 784 18215340 Power N-CT29^2T1T1 812 18741360 Power N-CT29^2T1 841 19267380 Power N-CT29^2 842 20504880 Add 1 factors 843 21189168 Add 2 factors 844 21417264 Add 3 factors 868 21449397 Power N-CT31^2T3 899 21975417 Power N-CT31^2T2 961 22276310 Power N-CT31^2 968 22568085 Martirosyan-TVT 1012 22590483 Martirosyan-TVT 1014 22612881 Martirosyan-TVT 1026 22647157 Martirosyan-TVT 1058 22654571 Martirosyan-TVT 1060 22838251 Martirosyan-TVT 1062 22850231 Martirosyan-TVT 1064 22860071 Martirosyan-TVT 1092 22918913 Martirosyan-TVT 1098 22953750 Martirosyan-TVT 1106 22966004 Martirosyan-TVT 1148 22967218 Martirosyan-TVT 1176 22972542 Martirosyan-TVT 1192 23062643 Martirosyan-TVT 1204 23588663 Martirosyan-TVT 1205 23644103 Martirosyan-TVT variant 1228 23699543 Martirosyan-TVT 1229 24188423 Martirosyan-TVT variant 1232 24311019 Martirosyan-Colbourn 1332 24477552 perfect hash family66,1332,12 1372 24503552 perfect hash family66,1600,14T2 1380 24503558 perfect hash family66,1600,14S2 1486 24503755 perfect hash family66,1600,14T1 1600 24503952 perfect hash family66,1600,14 1638 25811112 Power CT23^3T14T10T9 1764 25811309 Power CT23^3T14T9T9 1820 25833861 Power CT23^3T13T10T9 1960 25834058 Power CT23^3T13T9T9 2002 25836080 Power CT23^3T12T10T9 2156 25836277 Power CT23^3T12T9T9 2184 25838559 Power CT23^3T11T10T9 2197 25838565 Power CT23^3T10T10T10 2352 25838756 Power CT23^3T11T9T9 2366 25838762 Power CT23^3T10T10T9 2548 25838959 Power CT23^3T10T9T9 2744 25839156 Power CT23^3T9T9T9 2940 26100619 Power CT23^3T9T9T8 3150 26362082 Power CT23^3T9T8T8 3332 26516451 Power CT23^3T9T9T6 3528 26581108 Power CT23^3T9T9T5 3724 26581699 Power CT23^3T9T9T4 3920 26812673 Power CT23^3T9T9T3 4116 26815024 Power CT23^3T9T9T2 4312 26819116 Power CT23^3T9T9T1 4508 26841514 Power CT23^3T9T9 4620 27080579 Power CT23^3T9T8T1 4830 27102977 Power CT23^3T9T8 4900 27213268 Power CT25^3T11T11 5096 27253816 Power CT27^3T13T13T1 5292 27255030 Power CT27^3T13T13 5460 27515279 Power CT27^3T13T12T1 5670 27516493 Power CT27^3T13T12 5852 27561659 Power CT23^3T9T4T1 6118 27584057 Power CT23^3T9T4 6202 27754280 Power CT23^3T9S4 6482 27776678 Power CT23^3T9S3 6776 27799076 Power CT23^3T9T1T1 7084 27821474 Power CT23^3T9T1 7406 27843872 Power CT23^3T9 7590 28082937 Power CT23^3T8T1 7935 28105335 Power CT23^3T8 8050 28215626 Power CT25^3T11T2 8064 28232796 Power CT25^3T11T1T1 8400 28233994 Power CT25^3T11T1 8750 28235192 Power CT25^3T11 8778 28274296 Power CT27^3T13S4 9114 28275510 Power CT27^3T13S3 9464 28276724 Power CT27^3T13T1T1 9828 28277938 Power CT27^3T13T1 10000 28279152 Power CT27^3T13

Graph: