| k | N | Source |
| 4 | 5832 | Derive from strength 4 |
| 5 | 5994 | Li-Ji-Yin |
| 6 | 6156 | Ji-Yin |
| 20 | 6856 | orthogonal array fuse postop NCK |
| 24 | 11765 | orthogonal array fuse fuse fuse fuse fuse postop NCK |
| 40 | 12942 | Chateauneuf-Kreher doubling |
| 42 | 17885 | Chateauneuf-Kreher doubling |
| 76 | 18828 | Colbourn-Martirosyan-Trung-Walker |
| 95 | 18990 | Colbourn-Martirosyan-Trung-Walker |
| 114 | 19152 | Colbourn-Martirosyan-Trung-Walker |
| 120 | 19510 | Cohen-Colbourn-Ling |
| 380 | 19852 | Colbourn-Martirosyan-Trung-Walker |
| 1298 | 23364 | Cyclotomy (Colbourn) |
| 1423 | 25614 | Cyclotomy (Colbourn) |
| 1532 | 27576 | Cyclotomy (Colbourn) |
| 1550 | 27882 | Cyclotomy (Colbourn) |
| 1568 | 28206 | Cyclotomy (Colbourn) |
| 1622 | 29178 | Cyclotomy (Colbourn) |
| 1658 | 29826 | Cyclotomy (Colbourn) |
| 1693 | 30474 | Cyclotomy (Colbourn) |
| 1874 | 33714 | Cyclotomy (Colbourn) |
| 2000 | 35982 | Cyclotomy (Colbourn) |
| 2018 | 36306 | Cyclotomy (Colbourn) |
| 2054 | 36954 | Cyclotomy (Colbourn) |
| 2089 | 37602 | Cyclotomy (Colbourn) |
| 2166 | 38304 | Colbourn-Martirosyan-Trung-Walker |
| 2280 | 38662 | Colbourn-Martirosyan-Trung-Walker |
| 7220 | 39004 | Colbourn-Martirosyan-Trung-Walker |
| 7581 | 42516 | Colbourn-Martirosyan-Trung-Walker |
| 7600 | 42840 | Colbourn-Martirosyan-Trung-Walker |
| 8702 | 45072 | Colbourn-Martirosyan-Trung-Walker |
| 9063 | 45162 | Colbourn-Martirosyan-Trung-Walker |
| 9424 | 45198 | Colbourn-Martirosyan-Trung-Walker |
| 9785 | 45234 | Colbourn-Martirosyan-Trung-Walker |
| 10000 | 45288 | Colbourn-Martirosyan-Trung-Walker |