# Table for CAN(5,k,16) for k up to 10000

#### 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,16) 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 17 1048576 orthogonal array 18 1419855 orthogonal array fuse 19 2402895 Add 1 factors 20 2476093 orthogonal array fuse fuse fuse 24 3145725 perfect hash family3,24,17 34 4128768 Martirosyan-TVT 35 4769792 Martirosyan-TVT variant 36 5015552 Martirosyan-TVT 39 6291450 perfect hash family6,39,17 48 7340025 perfect hash family7,48,17 55 8388600 perfect hash family8,55,17 71 9437175 perfect hash family9,71,17 88 10485750 perfect hash family10,88,17 289 11534325 Power CT17^2 290 13891845 Add 1 factors 291 15796485 Add 2 factors 292 16779525 Add 3 factors 305 17762565 Add 16 factors 306 19093749 Add 17 factors 307 21079820 Power N-CT19^2Arc(3) 324 22062860 Power N-CT19^2T1T1 342 23045900 Power N-CT19^2T1 361 24028940 Power N-CT19^2 512 24386837 Martirosyan-TVT 544 24502037 Martirosyan-TVT 546 24693527 Martirosyan-TVT 547 25502999 Martirosyan-TVT variant 577 26312471 Martirosyan-TVT variant 578 26587515 Martirosyan-TVT 579 29214780 Martirosyan-TVT variant 580 29529116 Martirosyan-TVT 582 31433756 Martirosyan-TVT 584 32416796 Martirosyan-TVT 610 33399836 Martirosyan-TVT 612 34731020 Martirosyan-TVT 613 37256071 Martirosyan-TVT variant 614 37295363 Martirosyan-TVT 620 39634995 Power N-CT31^2T11 744 40304627 Power N-CT31^2T7 964 41287670 Power N-CT31^2+3 1026 45416437 Power CT32^2+2 1027 49843957 Add 1 factors 1044 50155510 Power N-CT37^2Arc(10) 1072 51431408 Power N-CT37^2Arc(9) 1101 52707306 Power N-CT37^2Arc(8) 1131 53983204 Power N-CT37^2Arc(7) 1162 55259102 Power N-CT37^2Arc(6) 1194 56535000 Power N-CT37^2Arc(5) 1235 57671625 perfect hash family55,1235,17 1261 59086796 Power N-CT37^2Arc(3) 4913 59768757 Power CT23^3T6T6T6 5202 60140036 Power CT23^3T6T6T5 5508 60511315 Power CT23^3T6T5T5 5832 60882594 Power CT23^3T5T5T5 6120 61567553 Power CT23^3T6T5T3 6156 61865634 Power CT23^3T5T5T4 6647 61865906 Power CT23^3T6T6 7038 62237185 Power CT23^3T6T5 7452 62608464 Power CT23^3T5T5 7820 63293423 Power CT23^3T6T3 7866 63591504 Power CT23^3T5T4 8280 63664702 Power CT23^3T5T3 8993 63963055 Power CT23^3T6 9522 64334334 Power CT23^3T5 10000 65317374 Power CT23^3T4
Graph: