| k | N | Source |
| 10 | 729 | orthogonal array |
| 12 | 1196 | orthogonal array fuse fuse postop NCK |
| 20 | 1377 | Chateauneuf-Kreher doubling |
| 41 | 1449 | Sherwood-Martirosyan-Colbourn |
| 90 | 2025 | Colbourn-Martirosyan-Trung-Walker |
| 113 | 2169 | Sherwood-Martirosyan-Colbourn |
| 114 | 2817 | Add a factor |
| 117 | 2865 | Colbourn-Martirosyan-Trung-Walker |
| 225 | 2889 | Sherwood-Martirosyan-Colbourn |
| 234 | 3257 | Colbourn-Martirosyan-Trung-Walker |
| 252 | 3265 | Colbourn-Martirosyan-Trung-Walker |
| 261 | 3273 | Colbourn-Martirosyan-Trung-Walker |
| 270 | 3281 | Colbourn-Martirosyan-Trung-Walker |
| 279 | 3313 | Colbourn-Martirosyan-Trung-Walker |
| 369 | 3321 | Colbourn-Martirosyan-Trung-Walker |
| 380 | 3411 | Cyclotomy (Colbourn) |
| 410 | 3474 | Cohen-Colbourn-Ling |
| 810 | 3897 | Colbourn-Martirosyan-Trung-Walker |
| 891 | 4041 | Colbourn-Martirosyan-Trung-Walker |
| 900 | 4097 | Colbourn-Martirosyan-Trung-Walker |
| 972 | 4177 | Colbourn-Martirosyan-Trung-Walker |
| 990 | 4209 | Colbourn-Martirosyan-Trung-Walker |
| 1017 | 4233 | Colbourn-Martirosyan-Trung-Walker |
| 1130 | 4518 | Cohen-Colbourn-Ling |
| 1161 | 4953 | Colbourn-Martirosyan-Trung-Walker |
| 1170 | 4993 | Colbourn-Martirosyan-Trung-Walker |
| 1260 | 5009 | Colbourn-Martirosyan-Trung-Walker |
| 1404 | 5057 | Colbourn-Martirosyan-Trung-Walker |
| 1422 | 5089 | Colbourn-Martirosyan-Trung-Walker |
| 1431 | 5097 | Colbourn-Martirosyan-Trung-Walker |
| 1440 | 5105 | Colbourn-Martirosyan-Trung-Walker |
| 1476 | 5113 | Colbourn-Martirosyan-Trung-Walker |
| 1494 | 5129 | Colbourn-Martirosyan-Trung-Walker |
| 1656 | 5145 | Colbourn-Martirosyan-Trung-Walker |
| 1728 | 5169 | Colbourn-Martirosyan-Trung-Walker |
| 1737 | 5177 | Colbourn-Martirosyan-Trung-Walker |
| 1746 | 5193 | Colbourn-Martirosyan-Trung-Walker |
| 1773 | 5201 | Colbourn-Martirosyan-Trung-Walker |
| 1791 | 5209 | Colbourn-Martirosyan-Trung-Walker |
| 1800 | 5217 | Colbourn-Martirosyan-Trung-Walker |
| 1827 | 5233 | Colbourn-Martirosyan-Trung-Walker |
| 1926 | 5241 | Colbourn-Martirosyan-Trung-Walker |
| 2025 | 5249 | Colbourn-Martirosyan-Trung-Walker |
| 2250 | 5562 | Cohen-Colbourn-Ling |
| 2268 | 5649 | Colbourn-Martirosyan-Trung-Walker |
| 2340 | 5657 | Colbourn-Martirosyan-Trung-Walker |
| 2349 | 5665 | Colbourn-Martirosyan-Trung-Walker |
| 2430 | 5673 | Colbourn-Martirosyan-Trung-Walker |
| 2502 | 5705 | Colbourn-Martirosyan-Trung-Walker |
| 2511 | 5713 | Colbourn-Martirosyan-Trung-Walker |
| 2592 | 5721 | Colbourn-Martirosyan-Trung-Walker |
| 2673 | 5729 | Colbourn-Martirosyan-Trung-Walker |
| 2700 | 5753 | Colbourn-Martirosyan-Trung-Walker |
| 2763 | 5761 | Colbourn-Martirosyan-Trung-Walker |
| 3321 | 5769 | Colbourn-Martirosyan-Trung-Walker |
| 3420 | 5859 | Colbourn-Martirosyan-Trung-Walker |
| 3690 | 5922 | Colbourn-Martirosyan-Trung-Walker |
| 4059 | 6066 | Cohen-Colbourn-Ling |
| 4100 | 6147 | Cohen-Colbourn-Ling |
| 4428 | 6338 | Cohen-Colbourn-Ling |
| 7290 | 6345 | Colbourn-Martirosyan-Trung-Walker |
| 8019 | 6489 | Colbourn-Martirosyan-Trung-Walker |
| 8100 | 6545 | Colbourn-Martirosyan-Trung-Walker |
| 8748 | 6625 | Colbourn-Martirosyan-Trung-Walker |
| 8829 | 6657 | Colbourn-Martirosyan-Trung-Walker |
| 8910 | 6713 | Colbourn-Martirosyan-Trung-Walker |
| 9000 | 6785 | Colbourn-Martirosyan-Trung-Walker |
| 9153 | 6817 | Colbourn-Martirosyan-Trung-Walker |
| 9828 | 7102 | Colbourn-Martirosyan-Trung-Walker |
| 10000 | 7158 | Colbourn-Martirosyan-Trung-Walker |