Table for CAN(5,k,20) 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,20) 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 3200000 Derive from strength 6 7 3542088 Augment OA 8 3724074 Augment OA 9 3912858 Augment OA 10 4107924 Augment OA 11 4308646 Augment OA 12 4514148 Augment OA 13 4723668 Augment OA 14 4935798 Augment OA 15 5150374 Augment OA 16 5365126 Augment OA 17 5578956 Augment OA 18 5789958 Augment OA 19 5996736 Augment OA 20 6197616 Augment OA 24 6436337 orthogonal array fuse fuse fuse 26 9765615 orthogonal array fuse fuse fuse fuse fuse 28 14348893 orthogonal array fuse fuse fuse fuse fuse fuse fuse 29 18802330 Martirosyan-TVT variant 30 18888970 Martirosyan-TVT 31 19232124 Martirosyan-TVT variant 32 19309008 perfect hash family3,32,24 33 19751531 Martirosyan-TVT variant 34 19899541 Martirosyan-TVT 35 20220762 Martirosyan-TVT variant 36 20240902 Martirosyan-TVT 38 20547145 Martirosyan-TVT 39 20835881 Martirosyan-TVT variant 40 21037281 Martirosyan-TVT 41 22231683 Martirosyan-TVT variant 42 23887063 Martirosyan-TVT 43 23892123 Martirosyan-TVT variant 44 23921183 Martirosyan-TVT 45 23927267 Martirosyan-TVT variant 46 23957375 Martirosyan-TVT 47 23964487 Martirosyan-TVT variant 48 24043755 Martirosyan-TVT 49 31104176 Martirosyan-TVT variant 50 32761107 Martirosyan-TVT 51 32766341 Martirosyan-TVT variant 52 32923651 Martirosyan-TVT 54 38415712 Power N-CT9^2T3 57 38562218 Power N-CT9^2Arc(3) 64 38751002 Power N-CT9^2T1T1 72 38939786 Power N-CT9^2T1 81 39128570 Power N-CT9^2 82 41079230 Power N-CT9^2+1 83 43086450 Power N-CT9^2+2 84 45141470 Power N-CT9^2+3 91 46792929 Power CT11^2Arc(3) 100 46993651 Power CT11^2T1T1 110 47194373 Power CT11^2T1 121 47395095 Power CT11^2 122 49655617 Power CT11^2+1 123 51122257 Power CT13^2Arc(4) 133 51331777 Power CT13^2Arc(3) 144 51541297 Power CT13^2T1T1 156 51750817 Power CT13^2T1 169 51960337 Power CT13^2 170 54293767 Power CT13^2+1 171 56654103 Power CT13^2+2 176 57252188 Power N-CT19^2T5S8 179 57259986 Power N-CT19^2T4S9 181 57428264 Power N-CT19^2Trin4,4,4 185 57458966 Power N-CT19^2T5S7 188 57466764 Power N-CT19^2T4S8 190 57474738 Power N-CT19^2T3S9 192 57643016 Power N-CT19^2Trin3,4,4 195 57665744 Power N-CT19^2T5S6 198 57673542 Power N-CT19^2T4S7 200 57681516 Power N-CT19^2T3S8 201 57688568 Power N-CT19^2T2S9 203 57856846 Power N-CT19^2Trin2,4,4 204 57857768 Power N-CT19^2Trin3,3,4 206 57872522 Power N-CT19^2Arc(5)T5 210 57880320 Power N-CT19^2Arc(6)T4 211 57888294 Power N-CT19^2T3S7 212 57895346 Power N-CT19^2T2S8 216 57899570 Power N-CT19^2Arc(10) 217 58072520 Power N-CT19^2Trin3,3,3 220 58087098 Power N-CT19^2Arc(5)T4 223 58095072 Power N-CT19^2Arc(6)T3 226 58106348 Power N-CT19^2Arc(9) 228 58282600 Power N-CT19^2Trin1,3,4 229 58285428 Power N-CT19^2Trin2,2,4 230 58286350 Power N-CT19^2Trin2,3,3 231 58293876 Power N-CT19^2Arc(4)T4 234 58301850 Power N-CT19^2Arc(5)T3 236 58308902 Power N-CT19^2Arc(6)T2 237 58313126 Power N-CT19^2Arc(8) 238 58488632 Power N-CT19^2T5T2 240 58489378 Power N-CT19^2T4T3 242 58496430 Power N-CT19^2Trin1,2,4 243 58497352 Power N-CT19^2Trin1,3,3 244 58500180 Power N-CT19^2Trin2,2,3 246 58508628 Power N-CT19^2Arc(4)T3 248 58515680 Power N-CT19^2Arc(5)T2 249 58519904 Power N-CT19^2Arc(7) 252 58699634 Power N-CT19^2T5T1 255 58703208 Power N-CT19^2T4T2 256 58704130 Power N-CT19^2T3T3 258 58711182 Power N-CT19^2Trin1,2,3 259 58714010 Power N-CT19^2Trin2,2,2 261 58722458 Power N-CT19^2Arc(4)T2 262 58726682 Power N-CT19^2Arc(6) 266 58906412 Power N-CT19^2T5 270 58914210 Power N-CT19^2T4T1 272 58917960 Power N-CT19^2T3T2 273 58922184 Power N-CT19^2Arc(2)T3 274 58925012 Power N-CT19^2Trin1,2,2 275 58929236 Power N-CT19^2Arc(3)T2 276 58933460 Power N-CT19^2Arc(5) 285 59120988 Power N-CT19^2T4 288 59128962 Power N-CT19^2T3T1 289 59131790 Power N-CT19^2T2T2 290 59136014 Power N-CT19^2Arc(2)T2 291 59140238 Power N-CT19^2Arc(4) 304 59335740 Power N-CT19^2T3 306 59342792 Power N-CT19^2T2T1 307 59347016 Power N-CT19^2Arc(3) 323 59549570 Power N-CT19^2T2 324 59553794 Power N-CT19^2T1T1 342 59760572 Power N-CT19^2T1 361 59967350 Power N-CT19^2 362 61976150 Power N-CT19^2+1 368 63292149 Power N-CT23^2T7 391 63505979 Power N-CT23^2T6 414 63716981 Power N-CT23^2T5 437 63923759 Power N-CT23^2T4 460 64124639 Power N-CT23^2T3 530 64363360 Power N-CT23^2+1 531 73607620 Add 1 factors 532 80797220 Add 2 factors 533 83837220 Add 3 factors 534 87406276 Add 4 factors 535 87718959 Add 5 factors 536 96963219 Add 5 factors 553 97433920 Power CT25^2Arc(3) 576 100763198 Power CT25^2T1T1 600 104092476 Power CT25^2T1 625 107421615 perfect hash family11,625,25,c fuse fuse fuse fuse fuse 626 107421754 Power CT25^2+1 627 119292574 Add 1 factors 628 126565774 Add 2 factors 643 126581529 Martirosyan-TVT variant 646 126630183 Martirosyan-TVT 648 126634407 Martirosyan-TVT 672 126841185 Martirosyan-TVT 673 127074296 Martirosyan-TVT variant 684 127366220 Martirosyan-TVT 720 127572998 Martirosyan-TVT 729 127592619 Power CT23^3T14T14T14 810 127787685 Power CT23^3T14T14T13 900 127982751 Power CT23^3T14T13T13 1000 128177817 Power CT23^3T13T13T13 1100 128378539 Power CT23^3T13T13T12 1210 128579261 Power CT23^3T13T12T12 2116 128726720 Power CT23^3Tlev 2197 130025049 Power CT23^3T10T10T10 2366 130237179 Power CT23^3T10T10T9 2548 130449309 Power CT23^3T10T9T9 2744 130661439 Power CT23^3T9T9T9 2940 130876015 Power CT23^3T9T9T8 2964 131088597 Power CT23^3T11T10T4 3150 131090591 Power CT23^3T9T8T8 3211 131298117 Power CT23^3T10T10T4 3276 131303469 Power CT23^3T10T9T5 3332 131304597 Power CT23^3T9T9T6 3375 131305167 Power CT23^3T8T8T8 3380 131498997 Power CT23^3T10T10T3 3458 131510247 Power CT23^3T10T9T4 3528 131515599 Power CT23^3T9T9T5 3570 131519173 Power CT23^3T9T8T6 3600 131519919 Power CT23^3T8T8T7 3640 131711127 Power CT23^3T10T9T3 3724 131722377 Power CT23^3T9T9T4 3780 131730175 Power CT23^3T9T8T5 3825 131733749 Power CT23^3T8T8T6 3840 131734671 Power CT23^3T8T7T7 3887 131737718 Power CT23^3T10T10 3920 131923257 Power CT23^3T9T9T3 3990 131936953 Power CT23^3T9T8T4 4050 131944751 Power CT23^3T8T8T5 4080 131948501 Power CT23^3T8T7T6 4096 131949423 Power CT23^3T7T7T7 4186 131949848 Power CT23^3T10T9 4200 132137833 Power CT23^3T9T8T3 4275 132151529 Power CT23^3T8T8T4 4284 132158757 Power CT23^3T9T6T5 4320 132159503 Power CT23^3T8T7T5 4508 132161978 Power CT23^3T9T9 4522 132365535 Power CT23^3T9T6T4 4560 132366281 Power CT23^3T8T7T4 4590 132373333 Power CT23^3T8T6T5 4608 132374255 Power CT23^3T7T7T5 4830 132376554 Power CT23^3T9T8 4845 132580111 Power CT23^3T8T6T4 4864 132581033 Power CT23^3T7T7T4 4896 132588085 Power CT23^3T7T6T5 4913 132590913 Power CT23^3T6T6T6 5175 132591130 Power CT23^3T8T8 5184 132799087 Power CT23^3T7T5T5 5244 132801266 Power CT23^3T11T4 5382 132804008 Power CT23^3T10T5 5474 132805136 Power CT23^3T9T6 5520 132805882 Power CT23^3T8T7 5681 133010786 Power CT23^3T10T4 5796 133016138 Power CT23^3T9T5 5865 133019712 Power CT23^3T8T6 5888 133020634 Power CT23^3T7T7 5980 133211666 Power CT23^3T10T3 6118 133222916 Power CT23^3T9T4 6210 133230714 Power CT23^3T8T5 6256 133234464 Power CT23^3T7T6 6348 133240867 Power CT23^3T11 6440 133423796 Power CT23^3T9T3 6555 133437492 Power CT23^3T8T4 6624 133445466 Power CT23^3T7T5 6647 133448294 Power CT23^3T6T6 6877 133450387 Power CT23^3T10 6900 133638372 Power CT23^3T8T3 6992 133652244 Power CT23^3T7T4 7038 133659296 Power CT23^3T6T5 7406 133662517 Power CT23^3T9 7429 133866074 Power CT23^3T6T4 7452 133870298 Power CT23^3T5T5 7935 133877093 Power CT23^3T8 8464 134091845 Power CT23^3T7 8993 134305675 Power CT23^3T6 9522 134516677 Power CT23^3T5 10000 134723455 Power CT23^3T4
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