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

Last Updated Sat Nov 16 19:19:53 MST 2019

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 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 35 19307231 CPHF Random Extension (CLS) 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 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 276 152745695 Add 13 factors 315 154457512 perfect hash family4,315,200 317 154457848 perfect hash family4,317,202 346 168937900 perfect hash family4,396,250T50 348 168937984 perfect hash family4,396,250T48 354 171062551 Martirosyan-TVT 355 171302335 Martirosyan-TVT variant 364 171542119 Martirosyan-TVT 365 171928987 Martirosyan-TVT variant 366 172315855 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 242720810 Add 1 factors 576 254163626 Add 2 factors 642 255820248 perfect hash family6,730,244T44 646 255820332 perfect hash family6,730,244T42 736 260647044 perfect hash family6,736,250 841 278469510 Power N-CT29^2 842 284038710 Power N-CT29^2+1 843 287808762 Power N-CT31^2Arc(4) 870 288122946 Power N-CT31^2T2T1 871 288151494 Power N-CT31^2Arc(3) 899 288465678 Power N-CT31^2T2 900 288494226 Power N-CT31^2T1T1 930 288836958 Power N-CT31^2T1 963 289179690 Power N-CT31^2+2 964 289605570 Power N-CT31^2+3 965 289608450 perfect hash family15,965,35 1025 308458336 Power CT32^2+1 1026 308912608 Power CT32^2+2 1027 308915680 Power CT32^2+3 1051 315227420 Power N-CT41^2Trin6,6,6 1089 319254452 Power N-CT41^2T8T8 1122 319282844 Power N-CT41^2T8T7 1155 319283036 Power N-CT41^2T8T6 1156 319311236 Power N-CT41^2T7T7 1190 319311428 Power N-CT41^2T7T6 1225 319311620 Power N-CT41^2T6T6 1230 323024504 Power N-CT41^2T11 1353 323367236 Power N-CT41^2T8 1394 323395628 Power N-CT41^2T7 1435 323395820 Power N-CT41^2T6 1681 327480020 Power N-CT41^2 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 2846 366179866 Power N-CT73^2Trin2,19,19 2862 366522442 Power N-CT73^2T20T19 2916 366522598 Power N-CT73^2T19T19 2971 369864274 Power N-CT73^2Trin8,8,22 3028 369890638 Power N-CT73^2Trin8,8,21 3085 369892666 Power N-CT73^2Trin8,8,20 3142 369892822 Power N-CT73^2Trin8,8,19 3229 370235554 Power N-CT73^2Trin2,8,22 3292 370261918 Power N-CT73^2Trin2,8,21 3355 370263946 Power N-CT73^2Trin2,8,20 3418 370264102 Power N-CT73^2Trin2,8,19 3445 370606678 Power N-CT73^2T20T8 3523 370606834 Power N-CT73^2Trin2,2,22 3592 370633198 Power N-CT73^2Trin2,2,21 3661 370635226 Power N-CT73^2Trin2,2,20 3730 370635382 Power N-CT73^2Trin2,2,19 3763 370977958 Power N-CT73^2T20T2 3834 370978114 Power N-CT73^2T19T2 3871 371265934 Power N-CT79^2T30 3942 371320846 Power N-CT73^2T19 3979 371584330 Power N-CT79^2Trin2,2,26 4054 371584486 Power N-CT79^2Trin2,2,25 4081 371610694 Power N-CT79^2T26T2 4158 371610850 Power N-CT79^2T25T2 4187 371637058 Power N-CT79^2T26 4266 371637214 Power N-CT79^2T25 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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