Table for CAN(6,k,12) for k up to 10000

Last Updated Wed Mar 9 06:22:05 MST 2022

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,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 7 2985984 composition 8 3546657 Augment OA 9 3859296 Augment OA 10 4191958 Augment OA 11 4542844 Augment OA 14 4826807 orthogonal array fuse 15 8225568 extended OA (Colbourn) special fuse 16 9651419 3-Restricted SCPHF RE (CL) fuse 20 14109119 5-Restricted SCPHF RE (CL) fuse 22 14451851 4-Restricted SCPHF RE (CL) fuse 23 14480399 SCPHF Random Extension (CLS) fuse 25 14480423 CPHF IPO 3 (WCS) fuse 29 18564635 5,5-Restricted SCPHF RE (CL) fuse 30 18935915 5-Restricted SCPHF RE (CL) fuse 33 19278647 4-Restricted SCPHF RE (CL) fuse 34 19307039 2-Restricted SCPHF RE (CL) fuse 39 19307231 CPHF IPO 4 (WCS) fuse 41 23391431 5,5-Restricted SCPHF RE (CL) fuse 49 23762711 5-Restricted SCPHF RE (CL) fuse 51 24105443 4-Restricted SCPHF RE (CL) fuse 52 24131807 3-Restricted SCPHF RE (CL) fuse 53 24133835 2-Restricted SCPHF RE (CL) fuse 54 24133991 SCPHF Random Extension (CLS) fuse 56 24134039 CPHF IPO 5 (WCS) fuse 59 27846947 5,5,5-Restricted SCPHF RE (CL) fuse 65 28218227 5,5-Restricted SCPHF RE (CL) fuse 71 28589507 5-Restricted SCPHF RE (CL) fuse 77 28932239 4-Restricted SCPHF RE (CL) fuse 81 28958603 3-Restricted SCPHF RE (CL) fuse 82 28960847 CPHF Random Extension (CLS) fuse 91 32673743 5,5,5-Restricted SCPHF RE (CL) fuse 102 33045023 5,5-Restricted SCPHF RE (CL) fuse 111 33416303 5-Restricted SCPHF RE (CL) fuse 121 33759035 4-Restricted SCPHF RE (CL) fuse 124 33785399 3-Restricted SCPHF RE (CL) fuse 200 38614379 SCPHF Random Extension (CLS) fuse 202 38614463 CPHF Random Extension (CLS) fuse 250 43441175 SCPHF Random Extension (CLS) fuse 251 62243123 Add 1 factors 252 73685939 Add 2 factors 253 80224691 Add 3 factors 255 88740837 Add 5 factors 256 92536975 Add 6 factors 263 97949447 Add 13 factors 264 116771987 Add 1 factors 265 128214803 Add 2 factors 266 134757299 Add 13 factors 268 143273445 Add 13 factors 269 147069583 Add 13 factors 280 151437905 Martirosyan-TVT 281 151727909 Martirosyan-TVT variant 286 152184865 Martirosyan-TVT 315 154457512 perfect hash family4,315,200 317 154457848 perfect hash family4,317,202 318 166097769 Martirosyan-TVT 319 166150317 Martirosyan-TVT variant 338 166203009 Martirosyan-TVT 339 166923729 Martirosyan-TVT variant 354 167921215 Martirosyan-TVT 355 168160999 Martirosyan-TVT variant 364 168400783 Martirosyan-TVT 365 168787651 Martirosyan-TVT variant 366 169174519 Martirosyan-TVT 396 173764696 perfect hash family4,396,250 444 193071890 perfect hash family5,444,200 446 193072226 perfect hash family5,450,202T2 450 193072310 perfect hash family5,450,202 451 206804391 Martirosyan-TVT variant 453 207089269 Martirosyan-TVT variant 455 209083415 Martirosyan-TVT variant 459 209368293 Martirosyan-TVT variant 470 211932195 Martirosyan-TVT 471 212089707 Martirosyan-TVT variant 474 212247795 Martirosyan-TVT 478 212379074 perfect hash family5,570,246T46 482 212379158 perfect hash family5,570,246T44 483 213107555 Martirosyan-TVT variant 484 213392433 Martirosyan-TVT 574 217205870 perfect hash family5,574,250 575 231686728 Power CT25^2T2 625 231686752 Power CT25^2 626 254306140 Add 1 factors 642 255820248 perfect hash family6,730,244T44 646 255820332 perfect hash family6,730,244T42 736 260647044 perfect hash family6,736,250 781 270301220 perfect hash family14,1107,40S14 801 274385420 perfect hash family14,1107,40S13 841 278469510 Power N-CT29^2 842 282553820 perfect hash family14,1107,40S11 850 284781450 Power N-CT37^2T12T3 851 284781618 Power N-CT37^2T14 925 284781642 Power N-CT37^2T12 930 288836958 Power N-CT31^2T1 957 288837270 Power N-CT37^2T8T4 986 288865662 Power N-CT37^2T8T3 1073 288865854 Power N-CT37^2T8 1110 289237134 Power N-CT37^2T7 1122 289579674 Power N-CT37^2T4T3 1221 289579866 Power N-CT37^2T4 1258 289608258 Power N-CT37^2T3 1371 289608450 Power N-CT37^2+2 1447 315227420 Power N-CT41^2Trin2,2,2 1521 319311620 Power N-CT41^2T2T2 1599 323395820 Power N-CT41^2T2 1681 327480020 Power N-CT41^2 1833 328222460 Power N-CT47^2T8 1927 332306660 Power N-CT47^2T6 2211 332677940 Power N-CT47^2+2 2221 336760304 Power N-CT53^2Trin4,4,4 2311 337103036 Power N-CT53^2Trin2,4,4 2356 337129400 Power N-CT53^2Trin1,4,4 2401 337131428 Power N-CT53^2T4T4 2405 337445768 Power N-CT53^2Trin2,2,4 2452 337472132 Power N-CT53^2Trin1,2,4 2499 337474160 Power N-CT53^2T4T2 2500 337498496 Power N-CT53^2Arc(2)T4 2548 337500524 Power N-CT53^2T4T1 2597 337502552 Power N-CT53^2T4 2601 337816892 Power N-CT53^2T2T2 2602 337841228 Power N-CT53^2Arc(2)T2 2652 337843256 Power N-CT53^2T2T1 2703 337845284 Power N-CT53^2T2 2704 337869620 Power N-CT53^2T1T1 2756 337871648 Power N-CT53^2T1 2809 337873676 Power N-CT53^2 2810 337875860 Power N-CT53^2+1 2812 337876532 Power N-CT53^2+3 2824 365808682 Power N-CT73^2Trin8,17,17 2842 366177730 Power N-CT73^2Trin2,17,21 2896 366179758 Power N-CT73^2Trin2,17,20 2950 366179914 Power N-CT73^2Trin2,17,19 3058 366179962 Power N-CT73^2Trin2,17,17 3136 366522694 Power N-CT73^2T17T17 3142 369892822 Power N-CT73^2Trin8,8,19 3256 369892870 Power N-CT73^2Trin8,8,17 3304 370235602 Power N-CT73^2T17T14 3355 370263946 Power N-CT73^2Trin2,8,20 3418 370264102 Power N-CT73^2Trin2,8,19 3544 370264150 Power N-CT73^2Trin2,8,17 3640 370606882 Power N-CT73^2T17T8 3661 370635226 Power N-CT73^2Trin2,2,20 3730 370635382 Power N-CT73^2Trin2,2,19 3868 370635430 Power N-CT73^2Trin2,2,17 3976 370978162 Power N-CT73^2T17T2 4088 371320894 Power N-CT73^2T17 4204 371584534 Power N-CT79^2Trin2,2,23 4312 371610898 Power N-CT79^2T23T2 4424 371637262 Power N-CT79^2T23 5748 372775858 Power N-CT83^2Arc(13)T2 5779 376382734 Power N-CT79^2Trin2,2,2 5929 376409098 Power N-CT79^2T2T2 6083 376435462 Power N-CT79^2T2 6243 376461826 Power N-CT79^2+2 6244 376490998 Power N-CT79^2+3 6253 395055478 Power N-CT83^2Arc(8) 6329 398768374 Power N-CT83^2Arc(7) 6406 402481270 Power N-CT83^2Arc(6) 6484 406194166 Power N-CT83^2Arc(5) 6563 409907062 Power N-CT83^2Arc(4) 6643 413619958 Power N-CT83^2Arc(3) 6724 417332854 Power N-CT83^2T1T1 6853 421017142 Power N-CT89^2T12 7209 421043506 Power N-CT89^2T8 7298 421045750 Power N-CT89^2T7 7923 424758646 Power N-CT89^2+2 8181 425498866 Power N-CT101^2T20 8282 425501110 Power N-CT101^2T19 9191 429214006 Power N-CT101^2T10 10000 429585286 Power N-CT101^2

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