Table for CAN(6,k,13) 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,13) 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 14 4826809 orthogonal array 15 9253764 extended OA (Colbourn) 16 9651421 3-Restricted SCPHF RE (CL) 20 14109121 5-Restricted SCPHF RE (CL) 22 14451853 4-Restricted SCPHF RE (CL) 23 14480401 SCPHF Random Extension (CLS) 29 18564637 5,5-Restricted SCPHF RE (CL) 30 18935917 5-Restricted SCPHF RE (CL) 33 19278649 4-Restricted SCPHF RE (CL) 34 19307041 2-Restricted SCPHF RE (CL) 35 19307233 CPHF Random Extension (CLS) 41 23391433 5,5-Restricted SCPHF RE (CL) 49 23762713 5-Restricted SCPHF RE (CL) 51 24105445 4-Restricted SCPHF RE (CL) 52 24131809 3-Restricted SCPHF RE (CL) 53 24133837 2-Restricted SCPHF RE (CL) 54 24133993 SCPHF Random Extension (CLS) 59 27846949 5,5,5-Restricted SCPHF RE (CL) 65 28218229 5,5-Restricted SCPHF RE (CL) 71 28589509 5-Restricted SCPHF RE (CL) 77 28932241 4-Restricted SCPHF RE (CL) 81 28958605 3-Restricted SCPHF RE (CL) 82 28960849 CPHF Random Extension (CLS) 91 32673745 5,5,5-Restricted SCPHF RE (CL) 102 33045025 5,5-Restricted SCPHF RE (CL) 111 33416305 5-Restricted SCPHF RE (CL) 121 33759037 4-Restricted SCPHF RE (CL) 124 33785401 3-Restricted SCPHF RE (CL) 200 38614381 SCPHF Random Extension (CLS) 202 38614465 CPHF Random Extension (CLS) 250 43441177 SCPHF Random Extension (CLS) 251 65661973 Add 1 factors 252 82261153 Add 2 factors 253 92094925 Add 3 factors 254 96550441 Add 4 factors 256 97769269 Add 13 factors 257 100975537 Add 13 factors 263 101005957 Add 13 factors 264 123251089 Add 13 factors 265 139850269 Add 13 factors 266 149974045 Add 13 factors 267 154455925 Add 13 factors 315 154457520 perfect hash family4,315,200 317 154457856 perfect hash family4,317,202 346 168937908 perfect hash family4,396,250T50 348 168937992 perfect hash family4,396,250T48 396 173764704 perfect hash family4,396,250 444 193071900 perfect hash family5,444,200 446 193072236 perfect hash family5,450,202T2 450 193072320 perfect hash family5,450,202 478 212379084 perfect hash family5,570,246T46 482 212379168 perfect hash family5,570,246T44 574 217205880 perfect hash family5,574,250 575 247360212 Add 1 factors 642 255820260 perfect hash family6,730,244T44 646 255820344 perfect hash family6,730,244T42 736 260647056 perfect hash family6,736,250 841 278469540 Power N-CT29^2 842 284038740 Power N-CT29^2+1 843 287808792 Power N-CT31^2Arc(4) 870 288122976 Power N-CT31^2T2T1 871 288151524 Power N-CT31^2Arc(3) 899 288465708 Power N-CT31^2T2 900 288494256 Power N-CT31^2T1T1 930 288836988 Power N-CT31^2T1 963 289179720 Power N-CT31^2+2 964 289605600 Power N-CT31^2+3 965 289608480 perfect hash family15,965,35 1025 308458368 Power CT32^2+1 1026 308912640 Power CT32^2+2 1027 308915712 Power CT32^2+3 1051 315227448 Power N-CT41^2Trin6,6,6 1089 319254480 Power N-CT41^2T8T8 1122 319282872 Power N-CT41^2T8T7 1155 319283064 Power N-CT41^2T8T6 1156 319311264 Power N-CT41^2T7T7 1190 319311456 Power N-CT41^2T7T6 1225 319311648 Power N-CT41^2T6T6 1230 323024532 Power N-CT41^2T11 1353 323367264 Power N-CT41^2T8 1394 323395656 Power N-CT41^2T7 1435 323395848 Power N-CT41^2T6 1681 327480048 Power N-CT41^2 1927 332306688 Power N-CT47^2T6 2211 332677968 Power N-CT47^2+2 2221 336760332 Power N-CT53^2Trin4,4,4 2311 337103064 Power N-CT53^2Trin2,4,4 2356 337129428 Power N-CT53^2Trin1,4,4 2401 337131456 Power N-CT53^2T4T4 2405 337445796 Power N-CT53^2Trin2,2,4 2452 337472160 Power N-CT53^2Trin1,2,4 2499 337474188 Power N-CT53^2T4T2 2500 337498524 Power N-CT53^2Arc(2)T4 2548 337500552 Power N-CT53^2T4T1 2597 337502580 Power N-CT53^2T4 2601 337816920 Power N-CT53^2T2T2 2602 337841256 Power N-CT53^2Arc(2)T2 2652 337843284 Power N-CT53^2T2T1 2703 337845312 Power N-CT53^2T2 2704 337869648 Power N-CT53^2T1T1 2756 337871676 Power N-CT53^2T1 2809 337873704 Power N-CT53^2 2810 337875888 Power N-CT53^2+1 2846 366179892 Power N-CT73^2Trin2,19,19 2862 366522468 Power N-CT73^2T20T19 2916 366522624 Power N-CT73^2T19T19 2971 369864300 Power N-CT73^2Trin8,8,22 3028 369890664 Power N-CT73^2Trin8,8,21 3085 369892692 Power N-CT73^2Trin8,8,20 3142 369892848 Power N-CT73^2Trin8,8,19 3229 370235580 Power N-CT73^2Trin2,8,22 3292 370261944 Power N-CT73^2Trin2,8,21 3355 370263972 Power N-CT73^2Trin2,8,20 3418 370264128 Power N-CT73^2Trin2,8,19 3445 370606704 Power N-CT73^2T20T8 3523 370606860 Power N-CT73^2Trin2,2,22 3592 370633224 Power N-CT73^2Trin2,2,21 3661 370635252 Power N-CT73^2Trin2,2,20 3730 370635408 Power N-CT73^2Trin2,2,19 3763 370977984 Power N-CT73^2T20T2 3834 370978140 Power N-CT73^2T19T2 3871 371265960 Power N-CT79^2T30 3942 371320872 Power N-CT73^2T19 3979 371584356 Power N-CT79^2Trin2,2,26 4054 371584512 Power N-CT79^2Trin2,2,25 4081 371610720 Power N-CT79^2T26T2 4158 371610876 Power N-CT79^2T25T2 4187 371637084 Power N-CT79^2T26 4266 371637240 Power N-CT79^2T25 5748 372775884 Power N-CT83^2Arc(13)T2 5779 376382760 Power N-CT79^2Trin2,2,2 5929 376409124 Power N-CT79^2T2T2 6083 376435488 Power N-CT79^2T2 6243 376461852 Power N-CT79^2+2 6244 376491024 Power N-CT79^2+3 6253 395055504 Power N-CT83^2Arc(8) 6329 398768400 Power N-CT83^2Arc(7) 6406 402481296 Power N-CT83^2Arc(6) 6484 406194192 Power N-CT83^2Arc(5) 6563 409907088 Power N-CT83^2Arc(4) 6643 413619984 Power N-CT83^2Arc(3) 6724 417332880 Power N-CT83^2T1T1 6853 421017168 Power N-CT89^2T12 7209 421043532 Power N-CT89^2T8 7298 421045776 Power N-CT89^2T7 7923 424758672 Power N-CT89^2+2 8181 425498892 Power N-CT101^2T20 8282 425501136 Power N-CT101^2T19 9191 429214032 Power N-CT101^2T10 10000 429585312 Power N-CT101^2

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