| k | N | Source |
| 10 | 531441 | orthogonal array |
| 11 | 997272 | extended OA (Colbourn) |
| 12 | 1469664 | Add a factor |
| 13 | 2356128 | Add a factor |
| 20 | 2598156 | Martirosyan-Tran van Trung |
| 21 | 3542292 | Add a factor |
| 22 | 4486428 | Add a factor |
| 23 | 5430564 | Add a factor |
| 24 | 6846444 | Add a factor |
| 25 | 8262324 | Add a factor |
| 26 | 8283195 | Martirosyan-Tran van Trung |
| 28 | 8735031 | Martirosyan-Tran van Trung |
| 30 | 8944839 | Martirosyan-Tran van Trung |
| 32 | 9154647 | Martirosyan-Tran van Trung |
| 34 | 9364455 | Martirosyan-Tran van Trung |
| 36 | 9469359 | Martirosyan-Tran van Trung |
| 38 | 9548037 | Martirosyan-Tran van Trung |
| 40 | 9626715 | Martirosyan-Tran van Trung |
| 41 | 11042595 | Add a factor |
| 42 | 11619927 | Martirosyan-Tran van Trung |
| 43 | 13824351 | Add a factor |
| 44 | 14698251 | Martirosyan-Tran van Trung |
| 46 | 16163055 | Martirosyan-Tran van Trung |
| 48 | 17578935 | Martirosyan-Tran van Trung |
| 50 | 18994815 | Martirosyan-Tran van Trung |
| 52 | 19015686 | Martirosyan-Tran van Trung |
| 56 | 19505538 | Martirosyan-Tran van Trung |
| 60 | 19753362 | Martirosyan-Tran van Trung |
| 64 | 20001186 | Martirosyan-Tran van Trung |
| 68 | 20249010 | Martirosyan-Tran van Trung |
| 72 | 20372922 | Martirosyan-Tran van Trung |
| 76 | 20465856 | Martirosyan-Tran van Trung |
| 78 | 20558790 | Martirosyan-Tran van Trung |
| 79 | 22763214 | Add a factor |
| 80 | 23910102 | Martirosyan-Tran van Trung |
| 81 | 26114526 | Add a factor |
| 82 | 26128638 | Martirosyan-Tran van Trung |
| 83 | 28333062 | Add a factor |
| 84 | 28706994 | Martirosyan-Tran van Trung |
| 85 | 31004730 | Add a factor |
| 88 | 32317182 | Martirosyan-Tran van Trung |
| 92 | 34233498 | Martirosyan-Tran van Trung |
| 96 | 35649378 | Martirosyan-Tran van Trung |
| 100 | 37065258 | Martirosyan-Tran van Trung |
| 104 | 37086129 | Martirosyan-Tran van Trung |
| 112 | 37613997 | Martirosyan-Tran van Trung |
| 120 | 37899837 | Martirosyan-Tran van Trung |
| 128 | 38185677 | Martirosyan-Tran van Trung |
| 136 | 38471517 | Martirosyan-Tran van Trung |
| 144 | 38614437 | Martirosyan-Tran van Trung |
| 152 | 38721627 | Martirosyan-Tran van Trung |
| 156 | 38828817 | Martirosyan-Tran van Trung |
| 190 | 39503765 | Power 19^2T9 |
| 209 | 39969596 | Power 19^2T8 |
| 228 | 40441988 | Power 19^2T7 |
| 247 | 41328452 | Power 19^2T6 |
| 362 | 41570480 | Power 19^2+1 |
| 363 | 46294904 | Add a factor |
| 364 | 51019328 | Add a factor |
| 365 | 55743752 | Add a factor |
| 366 | 60468176 | Add a factor |
| 367 | 65192600 | Add a factor |
| 368 | 69917024 | Add a factor |
| 369 | 74641448 | Add a factor |
| 373 | 79335920 | Power 23^2S8 |
| 378 | 79395344 | Martirosyan-Tran van Trung |
| 389 | 80280056 | Power 23^2S7 |
| 406 | 81224192 | Power 23^2S6 |
| 424 | 82168328 | Power 23^2S5 |
| 443 | 83112464 | Power 23^2S4 |
| 516 | 83140960 | perfect hash family32,516,20 |
| 529 | 86889008 | Power 23^2 |
| 544 | 88559883 | Martirosyan-Tran van Trung |
| 556 | 88578891 | Martirosyan-Tran van Trung |
| 560 | 88607403 | Martirosyan-Tran van Trung |
| 576 | 88616907 | Martirosyan-Tran van Trung |
| 596 | 88631163 | Martirosyan-Tran van Trung |
| 608 | 88669179 | Martirosyan-Tran van Trung |
| 624 | 88683435 | Martirosyan-Tran van Trung |
| 640 | 89384363 | Martirosyan-Tran van Trung |
| 702 | 89970771 | Martirosyan-Tran van Trung |
| 724 | 94899171 | Martirosyan-Tran van Trung |
| 725 | 99955371 | Add a factor |
| 726 | 101536491 | Martirosyan-Tran van Trung |
| 728 | 106341147 | Martirosyan-Tran van Trung |
| 730 | 111075075 | Martirosyan-Tran van Trung |
| 732 | 115799499 | Martirosyan-Tran van Trung |
| 734 | 120523923 | Martirosyan-Tran van Trung |
| 736 | 125248347 | Martirosyan-Tran van Trung |
| 738 | 129972771 | Martirosyan-Tran van Trung |
| 748 | 133409605 | Power N41^2T16S13 |
| 779 | 133430476 | Power N41^2T15S13 |
| 784 | 133752954 | Power N29^2T1T1 |
| 838 | 133882312 | Power N41^2T13S13 |
| 898 | 134092120 | Power N41^2T11S13 |
| 957 | 134301928 | Power N41^2T9S13 |
| 1016 | 134511736 | Power N41^2T7S13 |
| 1076 | 134616640 | Power N41^2T5S13 |
| 1134 | 134695318 | Power N41^2T3S13 |
| 1194 | 134773996 | Power N41^2S14 |
| 1223 | 136189876 | Power N41^2S13 |
| 1253 | 137605756 | Power N41^2S12 |
| 1284 | 139021636 | Power N41^2S11 |
| 1316 | 140437516 | Power N41^2S10 |
| 1348 | 141853396 | Power N41^2S9 |
| 1370 | 143220540 | Power N37^2+1 |
| 1381 | 143269276 | Power N41^2S8 |
| 1415 | 144685156 | Power N41^2S7 |
| 1450 | 146101036 | Power N41^2S6 |
| 1486 | 147516916 | Power N41^2S5 |
| 1523 | 148932796 | Power N41^2S4 |
| 1561 | 150348676 | Power N41^2S3 |
| 1600 | 151764556 | Power N41^2T1T1 |
| 1640 | 153180436 | Power N41^2T1 |
| 1681 | 154596316 | Power N41^2 |
| 1682 | 162249700 | Add a factor |
| 1683 | 169903084 | Add a factor |
| 1684 | 177556468 | Add a factor |
| 1685 | 185209852 | Add a factor |
| 1723 | 186927628 | Power N43^2S3 |
| 1764 | 189132052 | Power N43^2T1T1 |
| 1806 | 191336476 | Power N43^2T1 |
| 1849 | 193540900 | Power N43^2 |
| 1850 | 201666028 | Add a factor |
| 1851 | 209791156 | Add a factor |
| 1872 | 213789203 | Martirosyan-Tran van Trung |
| 1914 | 213955091 | Martirosyan-Tran van Trung |
| 1920 | 214164899 | Martirosyan-Tran van Trung |
| 1944 | 214202915 | Martirosyan-Tran van Trung |
| 1962 | 214854515 | Martirosyan-Tran van Trung |
| 1980 | 216312579 | Martirosyan-Tran van Trung |
| 2000 | 217770643 | Martirosyan-Tran van Trung |
| 2032 | 219228707 | Martirosyan-Tran van Trung |
| 2034 | 219333611 | Martirosyan-Tran van Trung |
| 2048 | 227441918 | Martirosyan-Tran van Trung |
| 2052 | 227479934 | Martirosyan-Tran van Trung |
| 2064 | 228063590 | Martirosyan-Tran van Trung |
| 2106 | 228101606 | Martirosyan-Tran van Trung |
| 2152 | 229488038 | Martirosyan-Tran van Trung |
| 2176 | 229566716 | Martirosyan-Tran van Trung |
| 2178 | 229585724 | Martirosyan-Tran van Trung |
| 2196 | 230876540 | Martirosyan-Tran van Trung |
| 2224 | 231078728 | Martirosyan-Tran van Trung |
| 2240 | 231107240 | Martirosyan-Tran van Trung |
| 2260 | 231116744 | Martirosyan-Tran van Trung |
| 2268 | 232203989 | Martirosyan-Tran van Trung |
| 2304 | 232698995 | Martirosyan-Tran van Trung |
| 2322 | 232713251 | Martirosyan-Tran van Trung |
| 2384 | 233351331 | Martirosyan-Tran van Trung |
| 2388 | 233389347 | Martirosyan-Tran van Trung |
| 2412 | 234805227 | Martirosyan-Tran van Trung |
| 2432 | 235019367 | Martirosyan-Tran van Trung |
| 2446 | 235033623 | Martirosyan-Tran van Trung |
| 2484 | 236449503 | Martirosyan-Tran van Trung |
| 2496 | 236889735 | Martirosyan-Tran van Trung |
| 2502 | 237590663 | Martirosyan-Tran van Trung |
| 2506 | 238074599 | Martirosyan-Tran van Trung |
| 2520 | 239490479 | Martirosyan-Tran van Trung |
| 2556 | 239652815 | Martirosyan-Tran van Trung |
| 2560 | 241339487 | Martirosyan-Tran van Trung |
| 2568 | 241925895 | Martirosyan-Tran van Trung |
| 2628 | 243341775 | Martirosyan-Tran van Trung |
| 2632 | 243498031 | Martirosyan-Tran van Trung |
| 2682 | 244913911 | Martirosyan-Tran van Trung |
| 2696 | 245568375 | Martirosyan-Tran van Trung |
| 2740 | 246935519 | Martirosyan-Tran van Trung |
| 2754 | 246984255 | Martirosyan-Tran van Trung |
| 2762 | 248252907 | Martirosyan-Tran van Trung |
| 2800 | 249668787 | Martirosyan-Tran van Trung |
| 2808 | 250091671 | Martirosyan-Tran van Trung |
| 2830 | 250792599 | Martirosyan-Tran van Trung |
| 2896 | 252208479 | Martirosyan-Tran van Trung |
| 2900 | 254121375 | Martirosyan-Tran van Trung |
| 2920 | 255216974 | Power N73^2T33 |
| 2952 | 255875823 | Martirosyan-Tran van Trung |
| 2993 | 256632854 | Power N73^2T32 |
| 3024 | 257117252 | Power N73^2T31T1 |
| 3066 | 257210186 | Power N73^2T31 |
| 3096 | 259321676 | Power N73^2T30T1 |
| 3139 | 259414610 | Power N73^2T30 |
| 3168 | 260195576 | Power N73^2T29T1 |
| 3212 | 260288510 | Power N73^2T29 |
| 3223 | 261474512 | Power N73^2T27S3 |
| 3267 | 261567446 | Power N73^2T27S2 |
| 3312 | 261660380 | Power N73^2T27T1 |
| 3358 | 261753314 | Power N73^2T27 |
| 3363 | 262890392 | Power N73^2T25S3 |
| 3409 | 262983326 | Power N73^2T25S2 |
| 3456 | 263076260 | Power N73^2T25T1 |
| 3504 | 263169194 | Power N73^2T25 |
| 3517 | 264073523 | Power N73^2T17S11 |
| 3545 | 264141275 | Power N73^2T21S5 |
| 3565 | 264166457 | Power N73^2T17S10 |
| 3716 | 264228413 | Power N73^2T13S12 |
| 3767 | 264321347 | Power N73^2T13S11 |
| 3819 | 264414281 | Power N73^2T13S10 |
| 3964 | 264476237 | Power N73^2T9S12 |
| 4019 | 264569171 | Power N73^2T9S11 |
| 4074 | 264662105 | Power N73^2T9S10 |
| 4211 | 264724061 | Power N73^2T5S12 |
| 4269 | 264816995 | Power N73^2T5S11 |
| 4458 | 264847973 | Power N73^2S13 |
| 4519 | 264940907 | Power N73^2S12 |
| 4581 | 265033841 | Power N73^2S11 |
| 4644 | 265126775 | Power N73^2S10 |
| 4708 | 265219709 | Power N73^2S9 |
| 4773 | 265312643 | Power N73^2S8 |
| 4839 | 265405577 | Power N73^2S7 |
| 4906 | 265498511 | Power N73^2S6 |
| 4974 | 265591445 | Power N73^2S5 |
| 5043 | 265684379 | Power N73^2S4 |
| 5113 | 265777313 | Power N73^2S3 |
| 5184 | 265870247 | Power N73^2T1T1 |
| 5256 | 265963181 | Power N73^2T1 |
| 5332 | 266056115 | Power N73^2+3 |
| 6400 | 268614329 | Power 32^3T22T12 |
| 7040 | 269080160 | Power 32^3T21T12 |
| 7680 | 269552552 | Power 32^3T20T12 |
| 8320 | 270439016 | Power 32^3T19T12 |
| 10000 | 270681044 | Power 31^3T11T11 |