Table for CAN(5,k,6) 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,6) 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 7776 Derive from strength 6 7 10368 Ji-Li-Yin 8 11664 Xu-Ji-Dong 9 19018 Density (Colbourn) postop NCK 10 22088 Density Cyclic (Colbourn) postop NCK 11 24730 Density Cyclic (Colbourn) postop NCK 12 27211 Density Cyclic (Colbourn) postop NCK 13 29357 Density Cyclic (Colbourn) postop NCK 14 31499 Density Cyclic (Colbourn) postop NCK 15 33545 Density Cyclic (Colbourn) postop NCK 16 35422 Density Cyclic (Colbourn) postop NCK 17 37203 Density Cyclic (Colbourn) postop NCK 18 38886 Density Cyclic (Colbourn) 19 40548 Density Cyclic (Colbourn) 20 42048 Density Cyclic (Colbourn) 21 43536 Density Cyclic (Colbourn) 22 45018 Density Cyclic (Colbourn) 23 46362 Density Cyclic (Colbourn) 24 47634 Density Cyclic (Colbourn) 25 48906 Density Cyclic (Colbourn) 26 53850 IPOG-F (NIST) 27 55069 IPOG-F (NIST) 28 56225 IPOG-F (NIST) 29 57363 IPOG-F (NIST) 30 58468 IPOG-F (NIST) 31 59529 IPOG-F (NIST) 32 60570 IPOG-F (NIST) 33 61562 IPOG-F (NIST) 34 62527 IPOG-F (NIST) 35 63471 IPOG-F (NIST) 36 64399 IPOG-F (NIST) 37 65292 IPOG-F (NIST) 38 66157 IPOG-F (NIST) 39 66997 IPOG-F (NIST) 40 67808 IPOG-F (NIST) 41 68609 IPOG-F (NIST) 42 69386 IPOG-F (NIST) 43 70148 IPOG-F (NIST) 44 70908 IPOG-F (NIST) 45 71645 IPOG-F (NIST) 46 72361 IPOG-F (NIST) 47 91081 AZ1 48 104581 Add 2 factors 49 123301 Add 2 factors 50 131207 Martirosyan-Colbourn 52 136781 Martirosyan-Colbourn 54 138750 Martirosyan-Colbourn 56 140446 Martirosyan-Colbourn 58 142274 Martirosyan-Colbourn 60 143949 Martirosyan-Colbourn 62 145640 Martirosyan-Colbourn 64 147221 Martirosyan-Colbourn 66 148813 Martirosyan-Colbourn 68 150228 Martirosyan-Colbourn 70 151652 Martirosyan-Colbourn 72 153120 Martirosyan-Colbourn 74 154523 Martirosyan-Colbourn 76 155868 Martirosyan-Colbourn 77 174588 AZ1 78 188808 Add 2 factors 80 198872 Martirosyan-Tran van Trung 82 201431 Martirosyan-Tran van Trung 84 202658 Martirosyan-Tran van Trung 86 205028 Martirosyan-Tran van Trung 88 206268 Martirosyan-Tran van Trung 90 207425 Martirosyan-Tran van Trung 92 208501 Martirosyan-Tran van Trung 93 227221 AZ1 94 227611 Martirosyan-Tran van Trung 96 241531 Martirosyan-Tran van Trung 97 260251 AZ1 98 260701 Martirosyan-Tran van Trung 99 266307 Power CT11^2T2 100 266735 Power CT11^2T1T1 110 269377 Power CT11^2T1 121 272019 Power CT11^2 124 290483 Martirosyan-Tran van Trung 126 292064 Martirosyan-Tran van Trung 128 293312 Martirosyan-Tran van Trung 130 296899 Martirosyan-Tran van Trung 132 298472 Martirosyan-Tran van Trung 134 300172 Martirosyan-Tran van Trung 136 300462 Martirosyan-Tran van Trung 138 302161 Martirosyan-Tran van Trung 140 303709 Martirosyan-Tran van Trung 142 305437 Martirosyan-Tran van Trung 144 305702 Martirosyan-Tran van Trung 146 307365 Martirosyan-Tran van Trung 148 307660 Martirosyan-Tran van Trung 150 309250 Martirosyan-Tran van Trung 152 310768 Martirosyan-Tran van Trung 156 320770 Power CT13^2T1 169 322916 Power CT13^2 170 346478 Power CT13^2+1 172 363751 Martirosyan-Colbourn 174 365236 Martirosyan-Colbourn 176 365456 Martirosyan-Colbourn 178 366853 Martirosyan-Colbourn 180 367058 Martirosyan-Colbourn 182 368354 Martirosyan-Colbourn 184 368569 Martirosyan-Colbourn 185 380077 Power CT16^2Arc(3)T2 186 380246 Power CT16^2Arc(5) 192 381420 Power CT16^2T4 195 381689 Power CT16^2T3T1 196 381785 Power CT16^2T2T2 197 381954 Power CT16^2Arc(2)T2 198 382123 Power CT16^2Arc(4) 208 383566 Power CT16^2T3 210 383831 Power CT16^2T2T1 211 384000 Power CT16^2Arc(3) 224 385708 Power CT16^2T2 225 385877 Power CT16^2T1T1 240 387754 Power CT16^2T1 256 389631 Power CT16^2 258 395337 Power N-CT19^2Trin1,2,3 259 395358 Power N-CT19^2Arc(3)T3 261 395477 Power N-CT19^2Arc(4)T2 262 395498 Power N-CT19^2Arc(6) 266 396421 Power N-CT19^2T5 270 396805 Power N-CT19^2T4T1 272 396999 Power N-CT19^2T3T2 273 397020 Power N-CT19^2Arc(2)T3 274 397118 Power N-CT19^2Trin1,2,2 275 397139 Power N-CT19^2Arc(3)T2 276 397160 Power N-CT19^2Arc(5) 285 398467 Power N-CT19^2T4 288 398682 Power N-CT19^2T3T1 289 398780 Power N-CT19^2T2T2 290 398801 Power N-CT19^2Arc(2)T2 291 398822 Power N-CT19^2Arc(4) 304 400344 Power N-CT19^2T3 306 400463 Power N-CT19^2T2T1 307 400484 Power N-CT19^2Arc(3) 323 402125 Power N-CT19^2T2 324 402146 Power N-CT19^2T1T1 342 403808 Power N-CT19^2T1 361 405470 Power N-CT19^2 362 420470 Power N-CT19^2+1 363 435350 Power N-CT19^2+2 364 450170 Power N-CT19^2+3 365 452144 Power N-CT23^2Trin2,2,4 366 452156 Power N-CT23^2Trin2,3,3 367 452420 Power N-CT23^2Arc(4)T4 370 452576 Power N-CT23^2Arc(5)T3 372 452720 Power N-CT23^2Arc(6)T2 373 452858 Power N-CT23^2Arc(8) 374 453107 Power N-CT23^2T6T1 378 453308 Power N-CT23^2T5T2 379 453446 Power N-CT23^2Arc(2)T5 380 453482 Power N-CT23^2T4T3 382 453626 Power N-CT23^2Trin1,2,4 383 453638 Power N-CT23^2Trin1,3,3 384 453644 Power N-CT23^2Trin2,2,3 386 453920 Power N-CT23^2Arc(4)T3 388 454064 Power N-CT23^2Arc(5)T2 389 454202 Power N-CT23^2Arc(7) 391 454451 Power N-CT23^2T6 396 454790 Power N-CT23^2T5T1 399 454970 Power N-CT23^2T4T2 400 454982 Power N-CT23^2T3T3 402 455126 Power N-CT23^2Trin1,2,3 403 455132 Power N-CT23^2Trin2,2,2 405 455408 Power N-CT23^2Arc(4)T2 406 455546 Power N-CT23^2Arc(6) 414 456134 Power N-CT23^2T5 418 456452 Power N-CT23^2T4T1 420 456470 Power N-CT23^2T3T2 421 456608 Power N-CT23^2Arc(2)T3 422 456614 Power N-CT23^2Trin1,2,2 423 456752 Power N-CT23^2Arc(3)T2 424 456890 Power N-CT23^2Arc(5) 437 457796 Power N-CT23^2T4 440 457952 Power N-CT23^2T3T1 441 457958 Power N-CT23^2T2T2 442 458096 Power N-CT23^2Arc(2)T2 443 458234 Power N-CT23^2Arc(4) 460 459296 Power N-CT23^2T3 462 459440 Power N-CT23^2T2T1 463 459578 Power N-CT23^2Arc(3) 483 460784 Power N-CT23^2T2 484 460922 Power N-CT23^2T1T1 506 462266 Power N-CT23^2T1 529 463610 Power N-CT23^2 530 476330 Power N-CT23^2+1 531 489050 Power N-CT23^2+2 532 532220 AZ1 550 534067 Power CT25^2T3 553 534139 Power CT25^2Arc(3) 576 535411 Power CT25^2T1T1 600 536683 Power CT25^2T1 625 537955 Power CT25^2 626 560459 Power N-CT29^2Trin1,2,5 627 560477 Power N-CT29^2Arc(3)T5 628 560512 Power N-CT29^2Trin1,3,4 629 560575 Power N-CT29^2Trin2,2,4 631 560611 Power N-CT29^2Arc(4)T4 638 561275 Power N-CT29^2T7 644 561481 Power N-CT29^2T6T1 648 561597 Power N-CT29^2T5T2 649 561615 Power N-CT29^2Arc(2)T5 650 561650 Power N-CT29^2T4T3 652 561731 Power N-CT29^2Trin1,2,4 653 561749 Power N-CT29^2Arc(3)T4 667 562619 Power N-CT29^2T6 672 562753 Power N-CT29^2T5T1 675 562869 Power N-CT29^2T4T2 676 562887 Power N-CT29^2Arc(2)T4 696 563891 Power N-CT29^2T5 700 564025 Power N-CT29^2T4T1 725 565163 Power N-CT29^2T4 728 568969 Power N-CT29^2T3T1 729 569032 Power N-CT29^2T2T2 730 569050 Power N-CT29^2Arc(2)T2 731 569068 Power N-CT29^2Arc(4) 754 570107 Power N-CT29^2T3 756 570188 Power N-CT29^2T2T1 757 570206 Power N-CT29^2Arc(3) 783 571326 Power N-CT29^2T2 784 571344 Power N-CT29^2T1T1 812 572482 Power N-CT29^2T1 841 573620 Power N-CT29^2 842 584670 Power N-CT29^2+1 1404 586454 Power N-CT47^2Arc(9)T11 1442 587347 Power N-CT47^2Arc(9)T10 1480 588212 Power N-CT47^2Arc(9)T9 1518 589052 Power N-CT47^2Arc(9)T8 1556 589863 Power N-CT47^2Arc(9)T7 1594 590664 Power N-CT47^2Arc(9)T6 1632 591441 Power N-CT47^2Arc(9)T5 1670 592203 Power N-CT47^2Arc(9)T4 1708 592963 Power N-CT47^2Arc(9)T3 1746 593700 Power N-CT47^2Arc(9)T2 1763 629784 Power N-CT43^2T2 1764 629799 Power N-CT43^2T1T1 1806 630561 Power N-CT43^2T1 1849 631323 Power N-CT43^2 1850 638163 Power N-CT43^2+1 1851 644796 Power N-CT43^2+2 1852 651240 Power N-CT43^2+3 1861 669960 Power N-CT47^2Arc(8) 1901 688680 Power N-CT47^2Arc(7) 1942 707400 Power N-CT47^2Arc(6) 1984 726120 Power N-CT47^2Arc(5) 2027 744840 Power N-CT47^2Arc(4) 2071 763560 Power N-CT47^2Arc(3) 2808 767197 Martirosyan-Colbourn 2814 768090 Martirosyan-Colbourn 2815 833610 AZ1 2816 859350 Add 2 factors 2817 907584 Add 3 factors 2818 919584 Add 4 factors 2849 925069 Power CT23^3T12S20 2893 926413 Power CT23^3T12S19 3108 927550 Power CT23^3T11S20 3156 928894 Power CT23^3T11S19 3367 929696 Power CT23^3T10S20 3419 931040 Power CT23^3T10S19 3626 931838 Power CT23^3T9S20 3682 933182 Power CT23^3T9S19 3885 933884 Power CT23^3T8S20 3945 935228 Power CT23^3T8S19 4144 935761 Power CT23^3T7S20 4208 937105 Power CT23^3T7S19 4403 937542 Power CT23^3T6S20 4471 938886 Power CT23^3T6S19 4662 939225 Power CT23^3T5S20 4734 940569 Power CT23^3T5S19 4921 940887 Power CT23^3T4S20 4997 942231 Power CT23^3T4S19 5180 942387 Power CT23^3T3S20 5260 943731 Power CT23^3T3S19 5439 943875 Power CT23^3T2S20 5523 945219 Power CT23^3T2S19 5698 945357 Power CT23^3S21 5786 946701 Power CT23^3S20 5896 948045 Power CT23^3S19 5901 949251 Power CT23^3T2S16 6028 949389 Power CT23^3S18 6069 950595 Power CT23^3T2S15 6182 950733 Power CT23^3S17 6258 951939 Power CT23^3T2S14 6358 952077 Power CT23^3S16 6380 953139 Power CT23^3T3S12 6468 953283 Power CT23^3T2S13 6556 953421 Power CT23^3S15 6620 954483 Power CT23^3T3S11 6699 954627 Power CT23^3T2S12 6776 954765 Power CT23^3S14 6802 955671 Power CT23^3T4S9 6804 955803 Power CT23^3T5T5T2 6880 955827 Power CT23^3T3S10 6951 955971 Power CT23^3T2S11 7018 956109 Power CT23^3S13 7038 956946 Power CT23^3T6T5 7040 956983 Power CT23^3T7T3T1 7056 956989 Power CT23^3T7T2T2 7087 957015 Power CT23^3T4S8 7160 957171 Power CT23^3T3S9 7224 957315 Power CT23^3T2S10 7282 957453 Power CT23^3S12 7308 958041 Power CT23^3T5S6 7360 958327 Power CT23^3T7T3 7391 958359 Power CT23^3T4S7 7392 958471 Power CT23^3T7T2T1 7460 958515 Power CT23^3T3S8 7518 958659 Power CT23^3T2S9 7568 958797 Power CT23^3S11 7581 959127 Power CT23^3T4T4T2 7600 959139 Power CT23^3T4T3T3 7632 959385 Power CT23^3T5S5 7714 959703 Power CT23^3T4S6 7728 959815 Power CT23^3T7T2 7780 959859 Power CT23^3T3S7 7833 960003 Power CT23^3T2S8 7876 960141 Power CT23^3S10 7920 960447 Power CT23^3T5T3T1 7938 960453 Power CT23^3T5T2T2 7942 960609 Power CT23^3T4T4T1 7980 960627 Power CT23^3T4T3T2 8000 960639 Power CT23^3T3T3T3 8056 961047 Power CT23^3T4S5 8120 961203 Power CT23^3T3S6 8169 961347 Power CT23^3T2S7 8206 961485 Power CT23^3S9 8211 961596 Power CT23^3T6T2 8228 961734 Power CT23^3T6T1T1 8280 961791 Power CT23^3T5T3 8316 961935 Power CT23^3T5T2T1 8334 962073 Power CT23^3T5S3 8360 962109 Power CT23^3T4T3T1 8379 962115 Power CT23^3T4T2T2 8400 962127 Power CT23^3T3T3T2 8417 962391 Power CT23^3T4S4 8480 962547 Power CT23^3T3S5 8526 962691 Power CT23^3T2S6 8558 962829 Power CT23^3S8 8602 963078 Power CT23^3T6T1 8694 963279 Power CT23^3T5T2 8712 963417 Power CT23^3T5T1T1 8740 963453 Power CT23^3T4T3 8778 963597 Power CT23^3T4T2T1 8800 963609 Power CT23^3T3T3T1 8820 963615 Power CT23^3T3T2T2 8860 963891 Power CT23^3T3S4 8904 964035 Power CT23^3T2S5 8932 964173 Power CT23^3S7 8993 964422 Power CT23^3T6 9108 964761 Power CT23^3T5T1 9177 964941 Power CT23^3T4T2 9200 964953 Power CT23^3T3T3 9240 965097 Power CT23^3T3T2T1 9261 965103 Power CT23^3T2T2T2 9303 965379 Power CT23^3T2S4 9328 965517 Power CT23^3S6 9522 966105 Power CT23^3T5 9614 966423 Power CT23^3T4T1 9660 966441 Power CT23^3T3T2 9680 966579 Power CT23^3T3T1T1 9702 966585 Power CT23^3T2T2T1 9723 966723 Power CT23^3T2S3 9746 966861 Power CT23^3S5 10000 967767 Power CT23^3T4

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