Table for CAN(6,k,19) 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,19) 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 20 47045881 orthogonal array 21 91485342 extended OA (Colbourn) 22 136055124 Add 1 factors 25 138661525 5-Restricted SCPHF RE (CL) 27 141007303 4-Restricted SCPHF RE (CL) 29 141137605 SCPHF Random Extension (CLS) 31 141137641 CPHF IPO 3 (WCS) 37 183231307 5,5-Restricted SCPHF RE (CL) 41 185707387 5-Restricted SCPHF RE (CL) 45 188053165 4-Restricted SCPHF RE (CL) 46 188183521 CPHF Random Extension (CLS) 59 230277169 5,5-Restricted SCPHF RE (CL) 65 232753249 5-Restricted SCPHF RE (CL) 70 235099027 4-Restricted SCPHF RE (CL) 74 235222489 3-Restricted SCPHF RE (CL) 76 235229401 CPHF Random Extension (CLS) 87 274846951 5,5,5-Restricted SCPHF RE (CL) 100 277323031 5,5-Restricted SCPHF RE (CL) 110 279799111 5-Restricted SCPHF RE (CL) 118 282144889 4-Restricted SCPHF RE (CL) 122 282268351 3-Restricted SCPHF RE (CL) 124 282274849 2-Restricted SCPHF RE (CL) 201 329321053 SCPHF Random Extension (CLS) 202 507599155 Add 1 factors 203 596615257 Add 2 factors 204 683409043 Add 3 factors 205 727978825 Add 4 factors 361 752733811 perfect hash family16,361,19,c 362 752734080 Power CT19^2+1 363 968422194 Add 1 factors 364 1057555260 Add 2 factors 365 1144349046 Add 3 factors 366 1188918828 Add 4 factors 380 1233488341 Add 19 factors 381 1233488610 Add 19 factors 382 1453855284 Add 19 factors 515 1505467603 perfect hash family32,515,19,c 516 1505468160 perfect hash family32,516,20 517 1728315702 Add 1 factors 518 1886379552 Add 2 factors 561 1975926312 perfect hash family6,561,201 580 2022972336 Power N-CT29^2T9 620 2022972840 Power N-CT31^2T11 651 2067412301 Power N-CT31^2T10 682 2111982083 Power N-CT31^2T9 725 2114587980 Power N-CT29^2T4 775 2114588484 Power N-CT31^2T6 783 2116933758 Power N-CT29^2T2 837 2116934262 Power N-CT31^2T4 841 2117064060 Power N-CT29^2 899 2117064564 Power N-CT31^2T2 961 2117064600 Power N-CT31^2 962 2384216874 Add 1 factors 973 2550381462 Power N-CT41^2Trin4,4,12 1039 2550381498 Power N-CT41^2Trin4,4,10 1073 2552857542 Power N-CT41^2T12T4 1147 2552857578 Power N-CT41^2T10T4 1189 2555333622 Power N-CT41^2T12 1271 2555333658 Power N-CT41^2T10 1333 2585828772 Power N-CT43^2T12 1369 2594951244 Power N-CT41^2T4T4 1517 2597427324 Power N-CT41^2T4 1681 2599903404 Power N-CT41^2 1763 2630398518 Power N-CT43^2T2 1851 2632744296 Power N-CT43^2+2 1852 2634569280 Power N-CT43^2+3 1861 2887131168 Power N-CT47^2Arc(8) 1901 2929224816 Power N-CT47^2Arc(7) 1946 2961214794 Power N-CT73^2Trin3,8,42 2015 2961338256 Power N-CT73^2T42T8 2025 2963553696 Power N-CT73^2T28T28 2086 2963560572 Power N-CT73^2Trin3,3,42 2170 2963684034 Power N-CT73^2T42T3 2263 2963807496 Power N-CT73^2T42 2266 3000962736 Power N-CT73^2Trin14,14,27 2407 3003308460 Power N-CT73^2Trin8,14,28 2419 3003431922 Power N-CT73^2T32T14 2458 3003438816 Power N-CT73^2Trin8,14,27 2562 3005654238 Power N-CT73^2Trin3,14,28 2655 3005777700 Power N-CT73^2T28T14 2701 3005901162 Power N-CT73^2T36 2714 3005908056 Power N-CT73^2T27T14 2814 3008130318 Power N-CT73^2Trin3,8,28 2925 3008253780 Power N-CT73^2T28T8 2993 3008377242 Power N-CT73^2T32 3024 3010476096 Power N-CT73^2Trin3,3,28 3150 3010599558 Power N-CT73^2T28T3 3285 3010723020 Power N-CT73^2T28 3358 3010853376 Power N-CT73^2T27 3481 3048001704 Power N-CT73^2T14T14 3682 3050354322 Power N-CT73^2Trin3,8,14 3835 3050477784 Power N-CT73^2T14T8 3962 3052700100 Power N-CT73^2Trin3,3,14 4130 3052823562 Power N-CT73^2T14T3 4307 3052947024 Power N-CT73^2T14 4364 3055176180 Power N-CT73^2Trin3,3,8 4550 3055299642 Power N-CT73^2T8T3 4745 3055423104 Power N-CT73^2T8 4900 3057645420 Power N-CT73^2T3T3 5110 3057768882 Power N-CT73^2T3 5330 3057892344 Power N-CT73^2+1 5332 3057982200 Power N-CT73^2+3 5411 3454150788 Power N-CT79^2Trin3,3,5 5557 3454157700 Power N-CT79^2Trin3,3,3 5624 3493768338 Power N-CT79^2T5T3 5776 3493775250 Power N-CT79^2T3T3 5810 3533262426 Power N-CT83^2T13 6142 3533385888 Power N-CT83^2T9 6308 3533392800 Power N-CT83^2T7 6464 3558153600 Power N-CT89^2Trin2,2,13 6612 3560629680 Power N-CT89^2T13T2 6790 3562975386 Power N-CT97^2T27 7178 3563098848 Power N-CT97^2T23 7372 3563105760 Power N-CT97^2T21 7378 3582914400 Power N-CT101^2Arc(4)T25 7451 3585390480 Power N-CT101^2Arc(3)T25 7525 3587866560 Power N-CT101^2Arc(2)T25 7600 3590342640 Power N-CT101^2T25T1 7630 3592688346 perfect hash family13,11881,109T39 8066 3592811808 perfect hash family13,11881,109T35 8284 3592818720 perfect hash family13,11881,109T33 8790 3602723310 Power N-CT101^2Arc(13)T2 9412 3605199390 Power N-CT97^2+3 9421 3617579790 Power N-CT101^2Arc(8) 9515 3620055870 Power N-CT101^2Arc(7) 9610 3622531950 Power N-CT101^2Arc(6) 9706 3625008030 Power N-CT101^2Arc(5) 9803 3627484110 Power N-CT101^2Arc(4) 9901 3629960190 Power N-CT101^2Arc(3) 10000 3632436270 Power N-CT101^2T1T1

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