Table for CAN(6,k,9) 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,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).

Change t: - Change v: - + or go to Global Menu.

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) 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) 27 2125761 CPHF Random Extension (CLS) 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) 39 3011481 5,5,5-Restricted SCPHF RE (CL) 44 3070521 5,5-Restricted SCPHF RE (CL) 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) 58 3542913 5,5,5-Restricted SCPHF RE (CL) 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 11109393 Add 3 factors 214 11581785 Add 4 factors 219 12054177 Add 9 factors 220 14828265 Add 9 factors 221 16607025 Add 9 factors 222 17849241 Add 9 factors 223 18321633 Add 9 factors 224 18794025 Add 9 factors 228 18799857 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+1 373 26040208 perfect hash family5,475,207T51 478 26571640 perfect hash family5,478,210 479 29869312 Add 1 factors 491 31354536 perfect hash family6,541,181T25 570 31885968 perfect hash family6,570,210 575 33795416 Power CT25^2T2 576 33801968 Power CT25^2T1T1 600 33854456 Power CT25^2T1 621 33894056 Power CT27^2T4 625 33906944 Power CT25^2 648 33953096 Power CT27^2T3 650 34004840 Power CT27^2T2T1 675 34005584 Power CT27^2T2 676 34010672 Power CT27^2T1T1 702 34011416 Power CT27^2T1 729 34012160 Power CT27^2 744 37613928 Power N-CT31^2T7 775 37666416 Power N-CT31^2T6 806 37672248 Power N-CT31^2T5 837 37672992 Power N-CT31^2T4 963 38086320 Power N-CT31^2+2 965 38971920 perfect hash family15,965,35 972 39310200 Power N-CT37^2T10T1 999 39316032 Power N-CT37^2T10 1031 39553680 Power N-CT37^2Trin2,4,4 1060 39606168 Power N-CT37^2Trin1,4,4 1089 39612000 Power N-CT37^2T4T4 1093 39612720 Power N-CT37^2Trin2,2,4 1124 39665208 Power N-CT37^2Trin1,2,4 1155 39671040 Power N-CT37^2T4T2 1159 39671760 Power N-CT37^2Trin2,2,2 1188 39723528 Power N-CT37^2T4T1 1192 39724248 Power N-CT37^2Trin1,2,2 1221 39729360 Power N-CT37^2T4 1225 39730080 Power N-CT37^2T2T2 1226 39776736 Power N-CT37^2Arc(2)T2 1260 39782568 Power N-CT37^2T2T1 1295 39788400 Power N-CT37^2T2 1296 39835056 Power N-CT37^2T1T1 1332 39840888 Power N-CT37^2T1 1369 39846720 Power N-CT37^2 1370 39857520 Power N-CT37^2+1 1374 42101536 Power N-CT41^2Trin2,3,3 1406 42159856 Power N-CT41^2T4T3 1444 42160576 Power N-CT41^2T3T3 1505 42514888 Power N-CT43^2T8 1548 42567376 Power N-CT43^2T7 1591 42573208 Power N-CT43^2T6 1634 42573928 Power N-CT43^2T5 1677 42928240 Power N-CT43^2T4 1850 42987280 Power N-CT43^2+1 1936 43695760 Power N-CT47^2T3T3 2068 43754800 Power N-CT47^2T3 2211 43813840 Power N-CT47^2+2 2221 44455360 Power N-CT53^2Trin4,4,4 2244 44507128 Power N-CT53^2T9T2 2311 44507848 Power N-CT53^2Trin2,4,4 2332 44512960 Power N-CT53^2T9 2401 44513680 Power N-CT53^2T4T4 2405 44560336 Power N-CT53^2Trin2,2,4 2499 44566168 Power N-CT53^2T4T2 2597 44572000 Power N-CT53^2T4 2601 44618656 Power N-CT53^2T2T2 2703 44624488 Power N-CT53^2T2 2809 44630320 Power N-CT53^2 2810 44639392 Power N-CT53^2+1 2811 44640400 Power N-CT53^2+2 2826 47231240 Power N-CT73^2Trin4,18,19 2877 47231312 Power N-CT73^2Trin4,18,18 2880 47283080 Power N-CT73^2Trin1,18,20 2881 47283656 Power N-CT73^2Trin1,19,19 2934 47283728 Power N-CT73^2Trin1,18,19 2988 47283800 Power N-CT73^2Trin1,18,18 3025 47289632 Power N-CT73^2T18T18 3051 47585552 Power N-CT73^2Trin9,9,19 3106 47585624 Power N-CT73^2Trin9,9,18 3150 47638112 Power N-CT73^2Trin1,15,18 3216 47643944 Power N-CT73^2Trin4,9,20 3276 47644592 Power N-CT73^2Trin4,9,19 3336 47644664 Power N-CT73^2Trin4,9,18 3348 47696432 Power N-CT73^2Trin1,9,20 3411 47697080 Power N-CT73^2Trin1,9,19 3474 47697152 Power N-CT73^2Trin1,9,18 3520 47702984 Power N-CT73^2T18T9 3526 47703632 Power N-CT73^2Trin4,4,19 3591 47703704 Power N-CT73^2Trin4,4,18 3608 47755472 Power N-CT73^2Trin1,4,20 3676 47756120 Power N-CT73^2Trin1,4,19 3744 47756192 Power N-CT73^2Trin1,4,18 3795 47762024 Power N-CT73^2T18T4 3801 47797016 Power N-CT73^2Arc(4)T18 3853 47802848 Power N-CT73^2Arc(3)T18 3906 47808680 Power N-CT73^2Arc(2)T18 3960 47814512 Power N-CT73^2T18T1 4015 47820344 Power N-CT73^2T18 4041 48110504 Power N-CT73^2Trin1,9,9 4096 48116336 Power N-CT73^2T9T9 4176 48117056 Power N-CT73^2Trin4,4,9 4356 48169544 Power N-CT73^2Trin1,4,9 4416 48175376 Power N-CT73^2T9T4 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

Graph: