| k | N | Source |
| 12 | 1331 | orthogonal array |
| 13 | 2079 | orthogonal array fuse fuse postop NCK |
| 14 | 2088 | orthogonal array fuse fuse postop NCK |
| 24 | 2541 | Chateauneuf-Kreher doubling |
| 50 | 2651 | Sherwood-Martirosyan-Colbourn |
| 132 | 3751 | Colbourn-Martirosyan-Trung-Walker |
| 146 | 3971 | Sherwood-Martirosyan-Colbourn |
| 398 | 4378 | Cyclotomy (Colbourn) |
| 419 | 4609 | Cyclotomy (Colbourn) |
| 420 | 5819 | Add a factor |
| 550 | 6171 | Colbourn-Martirosyan-Trung-Walker |
| 600 | 6402 | Cohen-Colbourn-Ling |
| 602 | 7222 | Cyclotomy (Colbourn) fuse |
| 1452 | 7271 | Colbourn-Martirosyan-Trung-Walker |
| 1573 | 7491 | Colbourn-Martirosyan-Trung-Walker |
| 1584 | 7581 | Colbourn-Martirosyan-Trung-Walker |
| 1606 | 7701 | Colbourn-Martirosyan-Trung-Walker |
| 1694 | 8108 | Colbourn-Martirosyan-Trung-Walker |
| 1705 | 8198 | Colbourn-Martirosyan-Trung-Walker |
| 1752 | 8206 | Cohen-Colbourn-Ling |
| 1848 | 8208 | Colbourn-Martirosyan-Trung-Walker |
| 1881 | 8268 | Colbourn-Martirosyan-Trung-Walker |
| 1947 | 8278 | Colbourn-Martirosyan-Trung-Walker |
| 1980 | 8288 | Colbourn-Martirosyan-Trung-Walker |
| 2101 | 8298 | Colbourn-Martirosyan-Trung-Walker |
| 2112 | 8308 | Colbourn-Martirosyan-Trung-Walker |
| 2233 | 8398 | Colbourn-Martirosyan-Trung-Walker |
| 2321 | 8458 | Colbourn-Martirosyan-Trung-Walker |
| 2442 | 8468 | Colbourn-Martirosyan-Trung-Walker |
| 2464 | 8478 | Colbourn-Martirosyan-Trung-Walker |
| 2475 | 8518 | Colbourn-Martirosyan-Trung-Walker |
| 2508 | 8528 | Colbourn-Martirosyan-Trung-Walker |
| 2552 | 8548 | Colbourn-Martirosyan-Trung-Walker |
| 2596 | 8558 | Colbourn-Martirosyan-Trung-Walker |
| 2805 | 8608 | Colbourn-Martirosyan-Trung-Walker |
| 2838 | 8618 | Colbourn-Martirosyan-Trung-Walker |
| 2849 | 8658 | Colbourn-Martirosyan-Trung-Walker |
| 2860 | 8668 | Colbourn-Martirosyan-Trung-Walker |
| 2882 | 8678 | Colbourn-Martirosyan-Trung-Walker |
| 2904 | 8688 | Colbourn-Martirosyan-Trung-Walker |
| 2970 | 8698 | Colbourn-Martirosyan-Trung-Walker |
| 3212 | 8728 | Colbourn-Martirosyan-Trung-Walker |
| 3223 | 8778 | Colbourn-Martirosyan-Trung-Walker |
| 3256 | 8788 | Colbourn-Martirosyan-Trung-Walker |
| 3344 | 8798 | Colbourn-Martirosyan-Trung-Walker |
| 3355 | 8848 | Colbourn-Martirosyan-Trung-Walker |
| 3399 | 8858 | Colbourn-Martirosyan-Trung-Walker |
| 3476 | 8868 | Colbourn-Martirosyan-Trung-Walker |
| 3564 | 8898 | Colbourn-Martirosyan-Trung-Walker |
| 3696 | 8908 | Colbourn-Martirosyan-Trung-Walker |
| 3828 | 8928 | Colbourn-Martirosyan-Trung-Walker |
| 3960 | 8938 | Colbourn-Martirosyan-Trung-Walker |
| 4125 | 8948 | Colbourn-Martirosyan-Trung-Walker |
| 4257 | 8958 | Colbourn-Martirosyan-Trung-Walker |
| 4356 | 8968 | Colbourn-Martirosyan-Trung-Walker |
| 4378 | 8978 | Colbourn-Martirosyan-Trung-Walker |
| 4532 | 9209 | Colbourn-Martirosyan-Trung-Walker |
| 4576 | 9219 | Colbourn-Martirosyan-Trung-Walker |
| 4609 | 9229 | Colbourn-Martirosyan-Trung-Walker |
| 4776 | 9339 | Cohen-Colbourn-Ling |
| 5028 | 9570 | Cohen-Colbourn-Ling |
| 5040 | 10780 | Cohen-Colbourn-Ling |
| 6050 | 10791 | Colbourn-Martirosyan-Trung-Walker |
| 6600 | 11022 | Colbourn-Martirosyan-Trung-Walker |
| 7150 | 11242 | Cohen-Colbourn-Ling |
| 7200 | 11363 | Cohen-Colbourn-Ling |
| 7300 | 11662 | Cohen-Colbourn-Ling |
| 10000 | 11891 | Colbourn-Martirosyan-Trung-Walker |