| k | N | Source |
| 17 | 1048576 | orthogonal array |
| 18 | 1419855 | orthogonal array fuse |
| 19 | 2402895 | Add a factor |
| 20 | 2476093 | orthogonal array fuse fuse fuse |
| 34 | 2531328 | Martirosyan-Tran van Trung |
| 36 | 3230912 | Martirosyan-Tran van Trung |
| 38 | 4919796 | Martirosyan-Tran van Trung |
| 40 | 5104258 | Martirosyan-Tran van Trung |
| 42 | 5581792 | Martirosyan-Tran van Trung |
| 44 | 5583744 | Martirosyan-Tran van Trung |
| 46 | 5589600 | Martirosyan-Tran van Trung |
| 56 | 5726240 | Martirosyan-Tran van Trung |
| 58 | 5755520 | Martirosyan-Tran van Trung |
| 60 | 5784800 | Martirosyan-Tran van Trung |
| 62 | 5814080 | Martirosyan-Tran van Trung |
| 64 | 5843360 | Martirosyan-Tran van Trung |
| 66 | 5872640 | Martirosyan-Tran van Trung |
| 68 | 6383135 | Martirosyan-Tran van Trung |
| 70 | 7194559 | Martirosyan-Tran van Trung |
| 72 | 7356529 | Martirosyan-Tran van Trung |
| 73 | 10182769 | Add a factor |
| 76 | 10341128 | Martirosyan-Tran van Trung |
| 88 | 10485750 | perfect hash family10,88,17 |
| 92 | 11288657 | Martirosyan-Tran van Trung |
| 112 | 11425297 | Martirosyan-Tran van Trung |
| 116 | 11454577 | Martirosyan-Tran van Trung |
| 120 | 11483857 | Martirosyan-Tran van Trung |
| 124 | 11513137 | Martirosyan-Tran van Trung |
| 289 | 11534325 | Power 17^2 |
| 290 | 14468565 | Add a factor |
| 291 | 16777200 | perfect hash family16,291,17 |
| 512 | 17233382 | Martirosyan-Tran van Trung |
| 544 | 17290982 | Martirosyan-Tran van Trung |
| 576 | 17675927 | Martirosyan-Tran van Trung |
| 578 | 18574742 | Martirosyan-Tran van Trung |
| 580 | 21676982 | Martirosyan-Tran van Trung |
| 582 | 23985617 | Martirosyan-Tran van Trung |
| 610 | 24441799 | Martirosyan-Tran van Trung |
| 612 | 24445703 | Martirosyan-Tran van Trung |
| 640 | 24963563 | Martirosyan-Tran van Trung |
| 964 | 25313270 | Power N31^2+3 |
| 984 | 26401879 | Martirosyan-Tran van Trung |
| 1012 | 26429207 | Martirosyan-Tran van Trung |
| 1018 | 26431159 | Martirosyan-Tran van Trung |
| 1024 | 26435063 | Martirosyan-Tran van Trung |
| 1056 | 26492663 | Martirosyan-Tran van Trung |
| 1064 | 27003158 | Martirosyan-Tran van Trung |
| 1088 | 27032438 | Martirosyan-Tran van Trung |
| 1102 | 27630473 | Martirosyan-Tran van Trung |
| 1120 | 27659753 | Martirosyan-Tran van Trung |
| 1140 | 27821723 | Martirosyan-Tran van Trung |
| 1152 | 27847099 | Martirosyan-Tran van Trung |
| 1156 | 30016549 | Martirosyan-Tran van Trung |
| 1160 | 33118789 | Martirosyan-Tran van Trung |
| 1164 | 35427424 | Martirosyan-Tran van Trung |
| 1190 | 35883606 | Martirosyan-Tran van Trung |
| 1196 | 36213156 | Martirosyan-Tran van Trung |
| 1220 | 36246576 | Martirosyan-Tran van Trung |
| 1224 | 36250480 | Martirosyan-Tran van Trung |
| 1280 | 37193200 | Martirosyan-Tran van Trung |
| 1734 | 37563217 | Martirosyan-Tran van Trung |
| 1928 | 37820632 | Martirosyan-Tran van Trung |
| 1968 | 38909241 | Martirosyan-Tran van Trung |
| 2024 | 38936569 | Martirosyan-Tran van Trung |
| 2036 | 38938521 | Martirosyan-Tran van Trung |
| 2048 | 38942425 | Martirosyan-Tran van Trung |
| 2112 | 39000025 | Martirosyan-Tran van Trung |
| 2128 | 39510520 | Martirosyan-Tran van Trung |
| 2176 | 39539800 | Martirosyan-Tran van Trung |
| 2204 | 40137835 | Martirosyan-Tran van Trung |
| 2240 | 40167115 | Martirosyan-Tran van Trung |
| 2280 | 40329085 | Martirosyan-Tran van Trung |
| 2304 | 40354461 | Martirosyan-Tran van Trung |
| 2312 | 42523911 | Martirosyan-Tran van Trung |
| 2320 | 45626151 | Martirosyan-Tran van Trung |
| 2328 | 47934786 | Martirosyan-Tran van Trung |
| 2380 | 48390968 | Martirosyan-Tran van Trung |
| 2392 | 48720518 | Martirosyan-Tran van Trung |
| 2440 | 48753938 | Martirosyan-Tran van Trung |
| 2448 | 48757842 | Martirosyan-Tran van Trung |
| 2560 | 49700562 | Martirosyan-Tran van Trung |
| 3468 | 50070579 | Martirosyan-Tran van Trung |
| 9248 | 50192363 | Power 32^3T15T15 |
| 9792 | 50563642 | Power 32^3T15T14 |
| 10000 | 50934921 | Power 31^3T13T13 |