| k | N | Source |
| 7 | 4096 | orthogonal array |
| 8 | 7225 | composition |
| 9 | 9191 | Density (Linnemann-Frewer) postop NCK |
| 10 | 11197 | Density (Colbourn) postop NCK |
| 11 | 13058 | Density (Linnemann-Frewer) postop NCK |
| 12 | 14888 | paintball (Kuhn) |
| 13 | 16384 | composition |
| 14 | 18360 | Density (Colbourn) postop NCK |
| 15 | 20191 | Density (Colbourn) postop NCK |
| 16 | 21524 | Density (Colbourn) postop NCK |
| 17 | 22758 | Density (Colbourn) postop NCK |
| 18 | 23931 | Density (Colbourn) postop NCK |
| 19 | 26392 | IPOG-F (NIST) |
| 20 | 27534 | IPOG-F (NIST) |
| 21 | 28625 | IPOG-F (NIST) |
| 22 | 29640 | IPOG-F (NIST) |
| 23 | 30636 | IPOG-F (NIST) |
| 24 | 31591 | IPOG-F (NIST) |
| 25 | 32501 | IPOG-F (NIST) |
| 26 | 33369 | IPOG-F (NIST) |
| 27 | 34187 | IPOG-F (NIST) |
| 28 | 35006 | IPOG-F (NIST) |
| 29 | 35791 | IPOG-F (NIST) |
| 30 | 36570 | IPOG-F (NIST) |
| 31 | 37305 | IPOG-F (NIST) |
| 32 | 38015 | IPOG-F (NIST) |
| 33 | 38695 | IPOG-F (NIST) |
| 34 | 39356 | IPOG-F (NIST) |
| 35 | 40002 | IPOG-F (NIST) |
| 36 | 40638 | IPOG-F (NIST) |
| 37 | 55806 | Add a factor |
| 38 | 70974 | Add a factor |
| 39 | 86142 | Add a factor |
| 40 | 101310 | Add a factor |
| 41 | 116478 | Add a factor |
| 42 | 125537 | Martirosyan-Tran van Trung |
| 44 | 127104 | Martirosyan-Tran van Trung |
| 46 | 128667 | Martirosyan-Tran van Trung |
| 48 | 130087 | Martirosyan-Tran van Trung |
| 50 | 137597 | Martirosyan-Tran van Trung |
| 52 | 140088 | Martirosyan-Tran van Trung |
| 54 | 141383 | Martirosyan-Tran van Trung |
| 56 | 142655 | Martirosyan-Tran van Trung |
| 58 | 143881 | Martirosyan-Tran van Trung |
| 60 | 147107 | Martirosyan-Tran van Trung |
| 62 | 150274 | Martirosyan-Tran van Trung |
| 64 | 167991 | Martirosyan-Tran van Trung |
| 66 | 169040 | Martirosyan-Tran van Trung |
| 68 | 170076 | Martirosyan-Tran van Trung |
| 70 | 173607 | Martirosyan-Tran van Trung |
| 72 | 174597 | Martirosyan-Tran van Trung |
| 74 | 190122 | Martirosyan-Tran van Trung |
| 76 | 205620 | Martirosyan-Tran van Trung |
| 77 | 212572 | Power 13^2T2S9 |
| 78 | 212906 | Power 13^2S11 |
| 80 | 213703 | Power 13^2T3S7 |
| 81 | 214068 | Power 13^2T2S8 |
| 82 | 214402 | Power 13^2S10 |
| 85 | 215199 | Power 13^2T3S6 |
| 87 | 215564 | Power 13^2T2S7 |
| 90 | 216695 | Power 13^2T3S5 |
| 92 | 217060 | Power 13^2T2S6 |
| 93 | 217394 | Power 13^2S8 |
| 96 | 218191 | Power 13^2T3S4 |
| 98 | 218556 | Power 13^2T2S5 |
| 99 | 218843 | Power 13^2T4T2 |
| 100 | 218988 | Power 13^2T3T3 |
| 103 | 219687 | Power 13^2T3S3 |
| 105 | 220052 | Power 13^2T2S4 |
| 106 | 220386 | Power 13^2S6 |
| 108 | 220673 | Power 13^2T4T1 |
| 110 | 220849 | Power 13^2T3T2 |
| 111 | 221183 | Power 13^2T3S2 |
| 113 | 221548 | Power 13^2T2S3 |
| 114 | 221882 | Power 13^2S5 |
| 117 | 222169 | Power 13^2T4 |
| 120 | 222679 | Power 13^2T3T1 |
| 121 | 222710 | Power 13^2T2T2 |
| 122 | 223044 | Power 13^2T2S2 |
| 123 | 223378 | Power 13^2S4 |
| 130 | 224175 | Power 13^2T3 |
| 132 | 224540 | Power 13^2T2T1 |
| 133 | 224874 | Power 13^2S3 |
| 143 | 226036 | Power 13^2T2 |
| 144 | 226370 | Power 13^2T1T1 |
| 156 | 227866 | Power 13^2T1 |
| 169 | 229362 | Power 13^2 |
| 170 | 251538 | Add a factor |
| 171 | 273714 | Add a factor |
| 172 | 292183 | Power 16^2T3S3 |
| 174 | 292826 | Power 16^2T2S4 |
| 176 | 292856 | Power 16^2T5 |
| 182 | 293018 | Power 16^2T3T2 |
| 183 | 293516 | Power 16^2T3S2 |
| 185 | 294159 | Power 16^2T2S3 |
| 186 | 294657 | Power 16^2S5 |
| 192 | 294686 | Power 16^2T4 |
| 195 | 294849 | Power 16^2T3T1 |
| 196 | 294994 | Power 16^2T2T2 |
| 197 | 295492 | Power 16^2T2S2 |
| 198 | 295990 | Power 16^2S4 |
| 208 | 296182 | Power 16^2T3 |
| 210 | 296825 | Power 16^2T2T1 |
| 211 | 297323 | Power 16^2S3 |
| 224 | 298158 | Power 16^2T2 |
| 225 | 298656 | Power 16^2T1T1 |
| 240 | 299989 | Power 16^2T1 |
| 256 | 301322 | Power 16^2 |
| 272 | 317364 | Power 17^2T1 |
| 289 | 318598 | Power 17^2 |
| 290 | 335020 | Power 17^2+1 |
| 291 | 357196 | Add a factor |
| 307 | 362091 | Power 19^2S3 |
| 324 | 364552 | Power 19^2T1T1 |
| 342 | 367013 | Power 19^2T1 |
| 361 | 369474 | Power 19^2 |
| 362 | 385462 | Power 19^2+1 |
| 363 | 400736 | Power 19^2+2 |
| 364 | 414946 | Power 19^2+3 |
| 368 | 419778 | Power 23^2T7 |
| 374 | 420016 | Power 23^2T6T1 |
| 378 | 420174 | Power 23^2T5T2 |
| 379 | 420193 | Power 23^2T5S2 |
| 391 | 421012 | Power 23^2T6 |
| 396 | 421189 | Power 23^2T5T1 |
| 414 | 422185 | Power 23^2T5 |
| 418 | 423650 | Power 23^2T4T1 |
| 420 | 423777 | Power 23^2T3T2 |
| 421 | 423796 | Power 23^2T3S2 |
| 423 | 423891 | Power 23^2T2S3 |
| 424 | 423910 | Power 23^2S5 |
| 437 | 424646 | Power 23^2T4 |
| 440 | 424792 | Power 23^2T3T1 |
| 441 | 424868 | Power 23^2T2T2 |
| 442 | 424887 | Power 23^2T2S2 |
| 443 | 424906 | Power 23^2S4 |
| 460 | 425788 | Power 23^2T3 |
| 462 | 425883 | Power 23^2T2T1 |
| 463 | 425902 | Power 23^2S3 |
| 483 | 426879 | Power 23^2T2 |
| 484 | 426898 | Power 23^2T1T1 |
| 506 | 427894 | Power 23^2T1 |
| 529 | 428890 | Power 23^2 |
| 530 | 442260 | Power 23^2+1 |
| 531 | 451360 | Power 25^2S4 |
| 550 | 452139 | Power 25^2T3 |
| 552 | 452225 | Power 25^2T2T1 |
| 553 | 452270 | Power 25^2S3 |
| 575 | 453135 | Power 25^2T2 |
| 576 | 453180 | Power 25^2T1T1 |
| 600 | 454090 | Power 25^2T1 |
| 625 | 455000 | Power 25^2 |
| 626 | 467152 | Power 25^2+1 |
| 627 | 475332 | Power 27^2S4 |
| 648 | 476008 | Power 27^2T3 |
| 650 | 476100 | Power 27^2T2T1 |
| 651 | 476150 | Power 27^2S3 |
| 675 | 476918 | Power 27^2T2 |
| 676 | 476968 | Power 27^2T1T1 |
| 702 | 477786 | Power 27^2T1 |
| 729 | 478604 | Power 27^2 |
| 730 | 490070 | Power 27^2+1 |
| 731 | 497920 | Power 29^2S4 |
| 754 | 498638 | Power 29^2T3 |
| 756 | 498671 | Power 29^2T2T1 |
| 757 | 498705 | Power 29^2S3 |
| 783 | 499456 | Power 29^2T2 |
| 784 | 499490 | Power 29^2T1T1 |
| 812 | 500275 | Power 29^2T1 |
| 841 | 501060 | Power 29^2 |
| 842 | 511966 | Power 29^2+1 |
| 843 | 519316 | Power 31^2S4 |
| 868 | 519957 | Power 31^2T3 |
| 870 | 520007 | Power 31^2T2T1 |
| 871 | 520051 | Power 31^2S3 |
| 899 | 520742 | Power 31^2T2 |
| 900 | 520786 | Power 31^2T1T1 |
| 930 | 521521 | Power 31^2T1 |
| 961 | 522256 | Power 31^2 |
| 992 | 531486 | Power 32^2T1 |
| 1024 | 532196 | Power 32^2 |
| 1025 | 541716 | Power 32^2+1 |
| 1026 | 550970 | Power 32^2+2 |
| 1027 | 560014 | Power 32^2+3 |
| 1028 | 568918 | Power 32^2 +4 |
| 1029 | 619270 | Add a factor |
| 1044 | 629590 | Power 37^2S10 |
| 1072 | 644758 | Power 37^2S9 |
| 1101 | 659926 | Power 37^2S8 |
| 1131 | 675094 | Power 37^2S7 |
| 1162 | 690262 | Power 37^2S6 |
| 1194 | 705430 | Power 37^2S5 |
| 1227 | 720598 | Power 37^2S4 |
| 1261 | 735766 | Power 37^2S3 |
| 1296 | 750934 | Power 37^2T1T1 |
| 1332 | 766102 | Power 37^2T1 |
| 1369 | 781270 | Power 37^2 |
| 1370 | 835474 | Add a factor |
| 1512 | 865969 | Power 27^3T20T19 |
| 1701 | 867935 | Power 27^3T20T18 |
| 1728 | 869098 | Power 27^3T19T19 |
| 1890 | 869941 | Power 27^3T20T17 |
| 1944 | 871064 | Power 27^3T19T18 |
| 2464 | 871663 | Power 27^3T20S26 |
| 2478 | 872481 | Power 27^3T20S25 |
| 2499 | 873299 | Power 27^3T20S24 |
| 2527 | 874117 | Power 27^3T20S23 |
| 2816 | 874792 | Power 27^3T19S26 |
| 2832 | 875610 | Power 27^3T19S25 |
| 2856 | 876428 | Power 27^3T19S24 |
| 3168 | 876758 | Power 27^3T18S26 |
| 3186 | 877576 | Power 27^3T18S25 |
| 3213 | 878394 | Power 27^3T18S24 |
| 3520 | 878764 | Power 27^3T17S26 |
| 3540 | 879582 | Power 27^3T17S25 |
| 3570 | 880400 | Power 27^3T17S24 |
| 3872 | 880625 | Power 27^3T16S26 |
| 3894 | 881443 | Power 27^3T16S25 |
| 3927 | 882261 | Power 27^3T16S24 |
| 4224 | 882455 | Power 27^3T15S26 |
| 4248 | 883273 | Power 27^3T15S25 |
| 4576 | 883951 | Power 27^3T14S26 |
| 4602 | 884769 | Power 27^3T14S25 |
| 4641 | 885587 | Power 27^3T14S24 |
| 4928 | 885927 | Power 27^3T13S26 |
| 4956 | 886745 | Power 27^3T13S25 |
| 4998 | 887563 | Power 27^3T13S24 |
| 5280 | 887758 | Power 27^3T12S26 |
| 5310 | 888576 | Power 27^3T12S25 |
| 5632 | 889091 | Power 27^3T11S26 |
| 5664 | 889909 | Power 27^3T11S25 |
| 5984 | 890325 | Power 27^3T10S26 |
| 6018 | 891143 | Power 27^3T10S25 |
| 6336 | 891498 | Power 27^3T9S26 |
| 6372 | 892316 | Power 27^3T9S25 |
| 6426 | 893134 | Power 27^3T9S24 |
| 6498 | 893952 | Power 27^3T9S23 |
| 6688 | 893959 | Power 27^3T8S26 |
| 6726 | 894777 | Power 27^3T8S25 |
| 7040 | 895101 | Power 27^3T7S26 |
| 7080 | 895919 | Power 27^3T7S25 |
| 7392 | 896192 | Power 27^3T6S26 |
| 7434 | 897010 | Power 27^3T6S25 |
| 7744 | 897207 | Power 27^3T5S26 |
| 7788 | 898025 | Power 27^3T5S25 |
| 8096 | 898203 | Power 27^3T4S26 |
| 8142 | 899021 | Power 27^3T4S25 |
| 8448 | 899158 | Power 27^3T3S26 |
| 8496 | 899976 | Power 27^3T3S25 |
| 8800 | 900068 | Power 27^3T2S26 |
| 8850 | 900886 | Power 27^3T2S25 |
| 9152 | 900936 | Power 27^3S27 |
| 9204 | 901754 | Power 27^3S26 |
| 9282 | 902572 | Power 27^3S25 |
| 9386 | 903390 | Power 27^3S24 |
| 9516 | 904208 | Power 27^3S23 |
| 9672 | 905026 | Power 27^3S22 |
| 9675 | 905794 | Power 27^3T2S19 |
| 9854 | 905844 | Power 27^3S21 |
| 9900 | 906612 | Power 27^3T2S18 |
| 10000 | 906662 | Power 27^3S20 |