Table for CAN(6,k,9) 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,9) 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 10 531441 orthogonal array 11 997272 extended OA (Colbourn) 12 1003833 5-Restricted SCPHF RE (CL) 13 1056321 4-Restricted SCPHF RE (CL) 14 1062873 SCPHF Random Extension (CLS) 18 1535265 5-Restricted SCPHF RE (CL) 19 1587753 4-Restricted SCPHF RE (CL) 20 1594305 SCPHF Random Extension (CLS) 21 1594321 CPHF IPO 3 (WCS) 23 2007657 5,5-Restricted SCPHF RE (CL) 24 2066697 5-Restricted SCPHF RE (CL) 25 2119185 4-Restricted SCPHF RE (CL) 26 2125017 3-Restricted SCPHF RE (CL) 31 2125761 CPHF IPO 4 (WCS) 33 2539089 5,5-Restricted SCPHF RE (CL) 35 2598129 5-Restricted SCPHF RE (CL) 36 2650617 4-Restricted SCPHF RE (CL) 37 2656449 3-Restricted SCPHF RE (CL) 38 2657169 SCPHF Random Extension (CLS) 44 2657201 CPHF IPO 5 (WCS) 49 3129561 5-Restricted SCPHF RE (CL) 51 3182049 4-Restricted SCPHF RE (CL) 53 3187881 3-Restricted SCPHF RE (CL) 54 3188529 2-Restricted SCPHF RE (CL) 55 3188601 SCPHF Random Extension (CLS) 61 3188641 CPHF IPO 6 (WCS) 64 3601953 5,5-Restricted SCPHF RE (CL) 69 3660993 5-Restricted SCPHF RE (CL) 72 3713481 4-Restricted SCPHF RE (CL) 75 3719313 3-Restricted SCPHF RE (CL) 76 3720033 SCPHF Random Extension (CLS) 78 3720081 CPHF Random Extension (CLS) 79 4015305 5+-Restricted SCPHF RE (CL) 83 4074345 5,5,5-Restricted SCPHF RE (CL) 92 4133385 5,5-Restricted SCPHF RE (CL) 99 4192425 5-Restricted SCPHF RE (CL) 107 4244913 4-Restricted SCPHF RE (CL) 108 4250745 3-Restricted SCPHF RE (CL) 112 4251393 2-Restricted SCPHF RE (CL) 156 4782897 SCPHF Random Extension (CLS) 210 5314329 SCPHF Random Extension (CLS) 211 8088417 Add 1 factors 212 9867177 Add 2 factors 213 11062737 Add 3 factors 214 11535129 Add 4 factors 219 12007521 Add 9 factors 220 14781609 Add 9 factors 221 16560369 Add 9 factors 222 17755929 Add 9 factors 223 18228321 Add 9 factors 228 18700713 Add 9 factors 243 19131584 perfect hash family4,243,156 278 20725880 perfect hash family4,332,210T54 332 21257312 perfect hash family4,332,210 335 23914480 perfect hash family5,335,156 337 24445912 perfect hash family5,345,157S4 339 24977344 perfect hash family5,345,157S3 342 25351544 Power CT19^2T1 361 25404032 Power CT19^2 362 25508864 Power CT19^2+1 363 25509120 Power CT19^2+2 373 26040208 perfect hash family5,475,207T51 478 26571640 perfect hash family5,478,210 479 29869312 Add 1 factors 483 31236856 Power N-CT29^2T8T6 504 31295896 Power N-CT29^2T8T5 558 31295904 Power N-CT31^2T13 589 31348392 Power N-CT31^2T12 620 31354944 Power N-CT31^2T11 651 31354960 Power N-CT31^2T10 713 31768296 Power N-CT31^2T8 744 31827336 Power N-CT31^2T7 775 31879824 Power N-CT31^2T6 806 31885656 Power N-CT31^2T5 961 31886400 Power N-CT31^2 962 35665032 Add 1 factors 1023 36551248 Power N-CT41^2T10T8 1085 36610288 Power N-CT41^2T10T6 1116 36662776 Power N-CT41^2T10T5 1147 36668608 Power N-CT41^2T10T4 1178 36669328 Power N-CT41^2T10T3 1333 36669360 Power N-CT43^2T12 1419 37082688 Power N-CT43^2T10 1505 37141728 Power N-CT43^2T8 1548 37194216 Power N-CT43^2T7 1591 37200048 Power N-CT43^2T6 1634 37200768 Power N-CT43^2T5 1850 37200800 Power N-CT43^2+1 1851 41918888 Add 1 factors 1936 42869120 Power N-CT47^2T3T3 2068 43341480 Power N-CT47^2T3 2211 43813840 Power N-CT47^2+2 2244 44093808 Power N-CT53^2T9T2 2332 44099640 Power N-CT53^2T9 2376 44109408 Power N-CT59^2T15T5 2420 44109480 Power N-CT59^2T15T4 2684 44109520 Power N-CT61^2T17 2695 44581840 Power N-CT59^2T10T4 2989 44581880 Power N-CT61^2T12 3111 44634368 Power N-CT61^2T10 3233 44640200 Power N-CT61^2T8 3294 44640848 Power N-CT61^2T7 3355 44640920 Power N-CT61^2T6 3721 44640960 Power N-CT61^2 3852 47697192 Power N-CT73^2Trin1,9,12 3904 47703024 Power N-CT73^2T12T9 3981 47703744 Power N-CT73^2Trin4,4,12 4152 47756232 Power N-CT73^2Trin1,4,12 4209 47762064 Power N-CT73^2T12T4 4215 47797056 Power N-CT73^2Arc(4)T12 4273 47802888 Power N-CT73^2Arc(3)T12 4332 47808720 Power N-CT73^2Arc(2)T12 4392 47814552 Power N-CT73^2T12T1 4453 47820384 Power N-CT73^2T12 4501 48176096 Power N-CT73^2Trin4,4,4 4545 48222032 Power N-CT73^2Arc(2)T9 4608 48227864 Power N-CT73^2T9T1 4696 48228584 Power N-CT73^2Trin1,4,4 4761 48234416 Power N-CT73^2T4T4 4767 48269408 Power N-CT73^2Arc(4)T4 4833 48275240 Power N-CT73^2Arc(3)T4 4900 48281072 Power N-CT73^2Arc(2)T4 4968 48286904 Power N-CT73^2T4T1 5037 48292736 Power N-CT73^2T4 5043 48327728 Power N-CT73^2Arc(4) 5113 48333560 Power N-CT73^2Arc(3) 5184 48339392 Power N-CT73^2T1T1 5256 48345224 Power N-CT73^2T1 5331 48351056 Power N-CT73^2+2 5332 48360416 Power N-CT73^2+3 5334 48361040 perfect hash family13,5334,78 5359 48656264 Power N-CT79^2Arc(12) 5427 48951488 Power N-CT79^2Arc(11) 5496 49246712 Power N-CT79^2Arc(10) 5566 49541936 Power N-CT79^2Arc(9) 5637 49837160 Power N-CT79^2Arc(8) 5709 50132384 Power N-CT79^2Arc(7) 5782 50427608 Power N-CT79^2Arc(6) 5856 50722832 Power N-CT79^2Arc(5) 5931 51018056 Power N-CT79^2Arc(4) 6007 51313280 Power N-CT79^2Arc(3) 6084 51608504 Power N-CT79^2T1T1 6162 51903728 Power N-CT79^2T1 6241 52198952 Power N-CT79^2 6308 52612160 Power N-CT83^2T7 6474 52612208 Power N-CT83^2T5 6557 52907432 Power N-CT83^2T4 6889 52966472 Power N-CT83^2 6942 53320688 Power N-CT89^2T11 7031 53615912 Power N-CT89^2T10 7387 53674952 Power N-CT89^2T6 7924 53733992 Power N-CT89^2+3 8029 54324392 Power N-CT97^2Trin5,5,5 8464 54383432 Power N-CT97^2T5T5 8924 54442472 Power N-CT97^2T5 9411 54501512 Power N-CT97^2+2 9607 55026392 Power N-CT101^2Trin2,2,2 9844 55072328 perfect hash family13,11449,107T15 10000 55131368 perfect hash family13,10609,103T4

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