| k | N | Source |
| 26 | 390625 | orthogonal array |
| 28 | 531437 | orthogonal array fuse fuse |
| 30 | 707273 | orthogonal array fuse fuse fuse fuse |
| 51 | 886875 | Derive from strength 5 |
| 52 | 1155601 | Colbourn-Martirosyan-Trung-Walker |
| 53 | 1224203 | Derive from strength 5 |
| 55 | 1224397 | Derive from strength 5 |
| 56 | 1393733 | Colbourn-Martirosyan-Trung-Walker |
| 75 | 1545625 | Colbourn-Martirosyan-Trung-Walker |
| 625 | 1905625 | Colbourn-Martirosyan-Trung-Walker |
| 650 | 2265625 | Colbourn-Martirosyan-Trung-Walker |
| 700 | 2503733 | Colbourn-Martirosyan-Trung-Walker |
| 750 | 2790473 | Colbourn-Martirosyan-Trung-Walker |
| 800 | 3095139 | Colbourn-Martirosyan-Trung-Walker |
| 1275 | 3121875 | Colbourn-Martirosyan-Trung-Walker |
| 1300 | 3390601 | Colbourn-Martirosyan-Trung-Walker |
| 1325 | 3610643 | Colbourn-Martirosyan-Trung-Walker |
| 1375 | 3610837 | Colbourn-Martirosyan-Trung-Walker |
| 1400 | 3780173 | Colbourn-Martirosyan-Trung-Walker |
| 1450 | 4046425 | Colbourn-Martirosyan-Trung-Walker |
| 1500 | 4047001 | Colbourn-Martirosyan-Trung-Walker |
| 1875 | 4140625 | Colbourn-Martirosyan-Trung-Walker |
| 10000 | 4500625 | Colbourn-Martirosyan-Trung-Walker |