| k | N | Source |
| 24 | 279841 | orthogonal array |
| 26 | 390621 | orthogonal array fuse fuse |
| 28 | 531433 | orthogonal array fuse fuse fuse fuse |
| 47 | 641677 | Derive from strength 5 |
| 48 | 826805 | Colbourn-Martirosyan-Trung-Walker |
| 51 | 886871 | Derive from strength 5 fuse fuse |
| 52 | 1013419 | Colbourn-Martirosyan-Trung-Walker |
| 69 | 1106139 | Colbourn-Martirosyan-Trung-Walker |
| 529 | 1362175 | Colbourn-Martirosyan-Trung-Walker |
| 552 | 1618211 | Colbourn-Martirosyan-Trung-Walker |
| 598 | 1804803 | Colbourn-Martirosyan-Trung-Walker |
| 625 | 1905621 | Colbourn-Martirosyan-Trung-Walker fuse fuse |
| 644 | 2033901 | Colbourn-Martirosyan-Trung-Walker |
| 1081 | 2236083 | Colbourn-Martirosyan-Trung-Walker |
| 1104 | 2421211 | Colbourn-Martirosyan-Trung-Walker |
| 1173 | 2599197 | Colbourn-Martirosyan-Trung-Walker |
| 1196 | 2725745 | Colbourn-Martirosyan-Trung-Walker |
| 1242 | 2908203 | Colbourn-Martirosyan-Trung-Walker |
| 1288 | 2909655 | Colbourn-Martirosyan-Trung-Walker |
| 1587 | 2956581 | Colbourn-Martirosyan-Trung-Walker |
| 10000 | 3212617 | Colbourn-Martirosyan-Trung-Walker |