| k | N | Source |
| 6 | 243 | orthogonal array |
| 7 | 351 | cross-sum (CKRS) |
| 8 | 405 | Xu-Ji-Dong |
| 10 | 483 | Derive from strength 6 |
| 11 | 705 | Density (Colbourn) postop NCK |
| 13 | 723 | Walker-Colbourn |
| 14 | 922 | Density (Linnemann-Frewer) postop NCK |
| 16 | 963 | Walker-Colbourn |
| 17 | 1117 | Density (Linnemann-Frewer) postop NCK |
| 18 | 1170 | Density (Linnemann-Frewer) postop NCK |
| 19 | 1203 | Walker-Colbourn |
| 20 | 1270 | Density (Linnemann-Frewer) postop NCK |
| 21 | 1322 | Density (Linnemann-Frewer) postop NCK |
| 22 | 1350 | Density (Linnemann-Frewer) postop NCK |
| 23 | 1409 | Density (Linnemann-Frewer) postop NCK |
| 24 | 1448 | Density (Linnemann-Frewer) postop NCK |
| 25 | 1488 | Density (Colbourn) postop NCK |
| 26 | 1521 | Density (Linnemann-Frewer) postop NCK |
| 27 | 1538 | Density (Linnemann-Frewer) postop NCK |
| 28 | 1579 | Density (Linnemann-Frewer) postop NCK |
| 29 | 1615 | Density (Linnemann-Frewer) postop NCK |
| 30 | 1647 | Density (Linnemann-Frewer) postop NCK |
| 31 | 1681 | Density (Linnemann-Frewer) postop NCK |
| 32 | 1724 | Density (Colbourn) postop NCK |
| 34 | 1783 | Density (Colbourn) postop NCK |
| 35 | 1851 | Density (Linnemann-Frewer) |
| 36 | 1882 | Density (Linnemann-Frewer) postop NCK |
| 37 | 1909 | Density (Linnemann-Frewer) |
| 38 | 1937 | Density (Linnemann-Frewer) postop NCK |
| 39 | 1960 | Density (Linnemann-Frewer) |
| 40 | 1986 | Density (Linnemann-Frewer) postop NCK |
| 41 | 2023 | IPOG-F (NIST) |
| 42 | 2046 | IPOG-F (NIST) |
| 43 | 2069 | IPOG-F (NIST) postop NCK |
| 44 | 2091 | IPOG-F (NIST) |
| 45 | 2112 | IPOG-F (NIST) |
| 46 | 2130 | IPOG-F (NIST) |
| 47 | 2150 | IPOG-F (NIST) |
| 48 | 2174 | IPOG-F (NIST) |
| 49 | 2191 | IPOG-F (NIST) |
| 50 | 2213 | IPOG-F (NIST) |
| 51 | 2231 | IPOG-F (NIST) |
| 52 | 2251 | IPOG-F (NIST) |
| 53 | 2269 | IPOG-F (NIST) |
| 54 | 2289 | IPOG-F (NIST) |
| 55 | 2309 | IPOG-F (NIST) |
| 56 | 2327 | IPOG-F (NIST) |
| 57 | 2342 | IPOG-F (NIST) |
| 58 | 2358 | IPOG-F (NIST) |
| 59 | 2373 | IPOG-F (NIST) |
| 60 | 2394 | IPOG-F (NIST) |
| 61 | 2408 | IPOG-F (NIST) |
| 62 | 2425 | IPOG-F (NIST) |
| 63 | 2440 | IPOG-F (NIST) |
| 64 | 2451 | IPOG-F (NIST) |
| 65 | 2468 | IPOG-F (NIST) |
| 66 | 2482 | IPOG-F (NIST) |
| 67 | 2498 | IPOG-F (NIST) |
| 68 | 2512 | IPOG-F (NIST) |
| 69 | 2527 | IPOG-F (NIST) |
| 70 | 2542 | IPOG-F (NIST) |
| 71 | 2555 | IPOG-F (NIST) |
| 72 | 2573 | IPOG-F (NIST) |
| 73 | 2584 | IPOG-F (NIST) |
| 74 | 2597 | IPOG-F (NIST) |
| 75 | 2609 | IPOG-F (NIST) |
| 76 | 2625 | IPOG-F (NIST) |
| 77 | 2639 | IPOG-F (NIST) |
| 78 | 2648 | IPOG-F (NIST) |
| 79 | 2661 | IPOG-F (NIST) |
| 80 | 2673 | IPOG-F (NIST) |
| 81 | 2686 | IPOG-F (NIST) |
| 82 | 2700 | IPOG-F (NIST) |
| 83 | 2710 | IPOG-F (NIST) |
| 84 | 2725 | IPOG-F (NIST) |
| 85 | 2739 | IPOG-F (NIST) |
| 86 | 2749 | IPOG-F (NIST) |
| 87 | 2762 | IPOG-F (NIST) |
| 88 | 2770 | IPOG-F (NIST) |
| 89 | 2783 | IPOG-F (NIST) |
| 90 | 2792 | IPOG-F (NIST) |
| 91 | 2805 | IPOG-F (NIST) |
| 92 | 2815 | IPOG-F (NIST) |
| 93 | 2825 | IPOG-F (NIST) |
| 94 | 2836 | IPOG-F (NIST) |
| 95 | 2847 | IPOG-F (NIST) |
| 96 | 2857 | IPOG-F (NIST) |
| 97 | 2868 | IPOG-F (NIST) |
| 98 | 2877 | IPOG-F (NIST) |
| 99 | 2885 | IPOG-F (NIST) |
| 100 | 2895 | IPOG-F (NIST) |
| 101 | 2909 | IPOG-F (NIST) |
| 102 | 2920 | IPOG-F (NIST) |
| 103 | 2928 | IPOG-F (NIST) |
| 104 | 2938 | IPOG-F (NIST) |
| 105 | 2945 | IPOG-F (NIST) |
| 106 | 2954 | IPOG-F (NIST) |
| 107 | 2962 | IPOG-F (NIST) |
| 108 | 2972 | IPOG-F (NIST) |
| 109 | 2980 | IPOG-F (NIST) |
| 110 | 2991 | IPOG-F (NIST) |
| 111 | 2999 | IPOG-F (NIST) |
| 112 | 3008 | IPOG-F (NIST) |
| 113 | 3017 | IPOG-F (NIST) |
| 114 | 3026 | IPOG-F (NIST) |
| 115 | 3036 | IPOG-F (NIST) |
| 116 | 3044 | IPOG-F (NIST) |
| 1051 | 3156 | Cyclotomy (Colbourn) |
| 1069 | 3210 | Cyclotomy (Colbourn) |
| 1087 | 3264 | Cyclotomy (Colbourn) |
| 1093 | 3282 | Cyclotomy (Colbourn) |
| 1123 | 3369 | Cyclotomy (Colbourn) |
| 1129 | 3390 | Cyclotomy (Colbourn) |
| 1171 | 3516 | Cyclotomy (Colbourn) |
| 1213 | 3642 | Cyclotomy (Colbourn) |
| 1231 | 3696 | Cyclotomy (Colbourn) |
| 1249 | 3750 | Cyclotomy (Colbourn) |
| 1250 | 5280 | Add a factor |
| 1251 | 6810 | Add a factor |
| 1508 | 6932 | Martirosyan-Tran van Trung |
| 1828 | 6986 | Martirosyan-Tran van Trung |
| 2102 | 7040 | Martirosyan-Tran van Trung |
| 2138 | 7130 | Martirosyan-Tran van Trung |
| 2174 | 7220 | Martirosyan-Tran van Trung |
| 2186 | 7250 | Martirosyan-Tran van Trung |
| 2234 | 7389 | Martirosyan-Tran van Trung |
| 2246 | 7397 | Martirosyan-Tran van Trung |
| 2258 | 7430 | Martirosyan-Tran van Trung |
| 2342 | 7640 | Martirosyan-Tran van Trung |
| 2426 | 7850 | Martirosyan-Tran van Trung |
| 2462 | 7940 | Martirosyan-Tran van Trung |
| 2498 | 8030 | Martirosyan-Tran van Trung |
| 2500 | 9620 | Martirosyan-Tran van Trung |
| 2502 | 11150 | Martirosyan-Tran van Trung |
| 2558 | 11272 | Martirosyan-Tran van Trung |
| 2582 | 11296 | Martirosyan-Tran van Trung |
| 2594 | 11308 | Martirosyan-Tran van Trung |
| 2606 | 11320 | Martirosyan-Tran van Trung |
| 2642 | 11360 | Martirosyan-Tran van Trung |
| 2654 | 11368 | Martirosyan-Tran van Trung |
| 2762 | 11476 | Martirosyan-Tran van Trung |
| 2798 | 11512 | Martirosyan-Tran van Trung |
| 2846 | 11560 | Martirosyan-Tran van Trung |
| 2858 | 11576 | Martirosyan-Tran van Trung |
| 2894 | 11608 | Martirosyan-Tran van Trung |
| 2906 | 11620 | Martirosyan-Tran van Trung |
| 2918 | 11632 | Martirosyan-Tran van Trung |
| 2942 | 11656 | Martirosyan-Tran van Trung |
| 2948 | 11680 | Martirosyan-Tran van Trung |
| 2966 | 11788 | Martirosyan-Tran van Trung |
| 2978 | 11800 | Martirosyan-Tran van Trung |
| 3016 | 11884 | Martirosyan-Tran van Trung |
| 3062 | 11938 | Martirosyan-Tran van Trung |
| 3086 | 11962 | Martirosyan-Tran van Trung |
| 3098 | 11974 | Martirosyan-Tran van Trung |
| 3134 | 12010 | Martirosyan-Tran van Trung |
| 3158 | 12034 | Martirosyan-Tran van Trung |
| 3194 | 12070 | Martirosyan-Tran van Trung |
| 3218 | 12094 | Martirosyan-Tran van Trung |
| 3242 | 12118 | Martirosyan-Tran van Trung |
| 3254 | 12130 | Martirosyan-Tran van Trung |
| 3314 | 12190 | Martirosyan-Tran van Trung |
| 3326 | 12202 | Martirosyan-Tran van Trung |
| 3338 | 12214 | Martirosyan-Tran van Trung |
| 3386 | 12262 | Martirosyan-Tran van Trung |
| 3398 | 12274 | Martirosyan-Tran van Trung |
| 3446 | 12322 | Martirosyan-Tran van Trung |
| 3482 | 12358 | Martirosyan-Tran van Trung |
| 3494 | 12370 | Martirosyan-Tran van Trung |
| 3506 | 12382 | Martirosyan-Tran van Trung |
| 3518 | 12394 | Martirosyan-Tran van Trung |
| 3554 | 12430 | Martirosyan-Tran van Trung |
| 3656 | 12436 | Martirosyan-Tran van Trung |
| 3872 | 12544 | Martirosyan-Tran van Trung |
| 3924 | 12556 | Martirosyan-Tran van Trung |
| 3960 | 12572 | Martirosyan-Tran van Trung |
| 4000 | 12588 | Martirosyan-Tran van Trung |
| 4204 | 12604 | Martirosyan-Tran van Trung |
| 4276 | 12730 | Martirosyan-Tran van Trung |
| 4348 | 12856 | Martirosyan-Tran van Trung |
| 4372 | 12898 | Martirosyan-Tran van Trung |
| 4468 | 13089 | Martirosyan-Tran van Trung |
| 4492 | 13105 | Martirosyan-Tran van Trung |
| 4516 | 13150 | Martirosyan-Tran van Trung |
| 4684 | 13444 | Martirosyan-Tran van Trung |
| 4728 | 13738 | Martirosyan-Tran van Trung |
| 4852 | 13792 | Martirosyan-Tran van Trung |
| 4924 | 13918 | Martirosyan-Tran van Trung |
| 4996 | 14044 | Martirosyan-Tran van Trung |
| 5000 | 15692 | Martirosyan-Tran van Trung |
| 5004 | 17222 | Martirosyan-Tran van Trung |
| 5082 | 17344 | Martirosyan-Tran van Trung |
| 5112 | 17346 | Martirosyan-Tran van Trung |
| 5116 | 17352 | Martirosyan-Tran van Trung |
| 5164 | 17376 | Martirosyan-Tran van Trung |
| 5188 | 17388 | Martirosyan-Tran van Trung |
| 5212 | 17400 | Martirosyan-Tran van Trung |
| 5284 | 17440 | Martirosyan-Tran van Trung |
| 5308 | 17448 | Martirosyan-Tran van Trung |
| 5346 | 17556 | Martirosyan-Tran van Trung |
| 5524 | 17572 | Martirosyan-Tran van Trung |
| 5596 | 17608 | Martirosyan-Tran van Trung |
| 5692 | 17656 | Martirosyan-Tran van Trung |
| 5716 | 17672 | Martirosyan-Tran van Trung |
| 5788 | 17704 | Martirosyan-Tran van Trung |
| 5808 | 17716 | Martirosyan-Tran van Trung |
| 5812 | 17728 | Martirosyan-Tran van Trung |
| 5836 | 17740 | Martirosyan-Tran van Trung |
| 5884 | 17764 | Martirosyan-Tran van Trung |
| 5886 | 17788 | Martirosyan-Tran van Trung |
| 5896 | 17804 | Martirosyan-Tran van Trung |
| 5932 | 17912 | Martirosyan-Tran van Trung |
| 5940 | 17924 | Martirosyan-Tran van Trung |
| 5956 | 17940 | Martirosyan-Tran van Trung |
| 6032 | 18024 | Martirosyan-Tran van Trung |
| 6060 | 18078 | Martirosyan-Tran van Trung |
| 6124 | 18132 | Martirosyan-Tran van Trung |
| 6172 | 18156 | Martirosyan-Tran van Trung |
| 6196 | 18168 | Martirosyan-Tran van Trung |
| 6268 | 18204 | Martirosyan-Tran van Trung |
| 6306 | 18228 | Martirosyan-Tran van Trung |
| 6316 | 18264 | Martirosyan-Tran van Trung |
| 6388 | 18300 | Martirosyan-Tran van Trung |
| 6414 | 18324 | Martirosyan-Tran van Trung |
| 6436 | 18360 | Martirosyan-Tran van Trung |
| 6484 | 18384 | Martirosyan-Tran van Trung |
| 6508 | 18396 | Martirosyan-Tran van Trung |
| 6522 | 18456 | Martirosyan-Tran van Trung |
| 6558 | 18468 | Martirosyan-Tran van Trung |
| 6628 | 18520 | Martirosyan-Tran van Trung |
| 6652 | 18532 | Martirosyan-Tran van Trung |
| 6676 | 18544 | Martirosyan-Tran van Trung |
| 6702 | 18592 | Martirosyan-Tran van Trung |
| 6738 | 18600 | Martirosyan-Tran van Trung |
| 6772 | 18612 | Martirosyan-Tran van Trung |
| 6774 | 18624 | Martirosyan-Tran van Trung |
| 6796 | 18708 | Martirosyan-Tran van Trung |
| 6892 | 18756 | Martirosyan-Tran van Trung |
| 6964 | 18792 | Martirosyan-Tran van Trung |
| 6966 | 18804 | Martirosyan-Tran van Trung |
| 6988 | 18820 | Martirosyan-Tran van Trung |
| 7012 | 18832 | Martirosyan-Tran van Trung |
| 7026 | 18844 | Martirosyan-Tran van Trung |
| 7036 | 18928 | Martirosyan-Tran van Trung |
| 7108 | 18964 | Martirosyan-Tran van Trung |
| 7278 | 18970 | Martirosyan-Tran van Trung |
| 7312 | 19006 | Martirosyan-Tran van Trung |
| 7386 | 19114 | Martirosyan-Tran van Trung |
| 7494 | 19150 | Martirosyan-Tran van Trung |
| 7532 | 19210 | Martirosyan-Tran van Trung |
| 7668 | 19264 | Martirosyan-Tran van Trung |
| 7674 | 19276 | Martirosyan-Tran van Trung |
| 7744 | 19300 | Martirosyan-Tran van Trung |
| 7746 | 19312 | Martirosyan-Tran van Trung |
| 7782 | 19324 | Martirosyan-Tran van Trung |
| 7818 | 19336 | Martirosyan-Tran van Trung |
| 7848 | 19376 | Martirosyan-Tran van Trung |
| 7920 | 19392 | Martirosyan-Tran van Trung |
| 7926 | 19408 | Martirosyan-Tran van Trung |
| 7962 | 19416 | Martirosyan-Tran van Trung |
| 7992 | 19524 | Martirosyan-Tran van Trung |
| 7998 | 19596 | Martirosyan-Tran van Trung |
| 8000 | 19652 | Martirosyan-Tran van Trung |
| 8088 | 19668 | Martirosyan-Tran van Trung |
| 8286 | 19672 | Martirosyan-Tran van Trung |
| 8316 | 19708 | Martirosyan-Tran van Trung |
| 8408 | 19724 | Martirosyan-Tran van Trung |
| 8552 | 19886 | Martirosyan-Tran van Trung |
| 8696 | 20048 | Martirosyan-Tran van Trung |
| 8744 | 20102 | Martirosyan-Tran van Trung |
| 8936 | 20345 | Martirosyan-Tran van Trung |
| 8984 | 20369 | Martirosyan-Tran van Trung |
| 9032 | 20426 | Martirosyan-Tran van Trung |
| 9368 | 20804 | Martirosyan-Tran van Trung |
| 9456 | 21182 | Martirosyan-Tran van Trung |
| 9704 | 21236 | Martirosyan-Tran van Trung |
| 9848 | 21398 | Martirosyan-Tran van Trung |
| 9992 | 21560 | Martirosyan-Tran van Trung |
| 10000 | 23236 | Power N101^2T1T1 |