| k | N | Source |
| 20 | 130321 | orthogonal array |
| 21 | 253422 | extended orthogonal array (Colbourn) |
| 24 | 279833 | orthogonal array fuse fuse fuse fuse |
| 39 | 306489 | Derive from strength 5 |
| 40 | 383725 | Colbourn-Martirosyan-Trung-Walker |
| 57 | 513703 | Colbourn-Martirosyan-Trung-Walker |
| 60 | 623143 | Colbourn-Martirosyan-Trung-Walker |
| 361 | 630667 | Colbourn-Martirosyan-Trung-Walker |
| 380 | 734635 | Colbourn-Martirosyan-Trung-Walker |
| 400 | 856946 | Colbourn-Martirosyan-Trung-Walker |
| 418 | 974219 | Colbourn-Martirosyan-Trung-Walker |
| 437 | 974687 | Colbourn-Martirosyan-Trung-Walker |
| 456 | 975371 | Colbourn-Martirosyan-Trung-Walker |
| 665 | 1027767 | Colbourn-Martirosyan-Trung-Walker |
| 741 | 1040763 | Colbourn-Martirosyan-Trung-Walker |
| 760 | 1117999 | Colbourn-Martirosyan-Trung-Walker |
| 780 | 1267762 | Colbourn-Martirosyan-Trung-Walker |
| 800 | 1344998 | Colbourn-Martirosyan-Trung-Walker |
| 1083 | 1364941 | Colbourn-Martirosyan-Trung-Walker |
| 1140 | 1474381 | Colbourn-Martirosyan-Trung-Walker |
| 6859 | 1481905 | Colbourn-Martirosyan-Trung-Walker |
| 6860 | 1563840 | Power N-CT19^3+1 |
| 6878 | 1690200 | Colbourn-Martirosyan-Trung-Walker |
| 6973 | 1694197 | Colbourn-Martirosyan-Trung-Walker |
| 6992 | 1694556 | Colbourn-Martirosyan-Trung-Walker |
| 7106 | 1694563 | Colbourn-Martirosyan-Trung-Walker |
| 7220 | 1698997 | Colbourn-Martirosyan-Trung-Walker |
| 7334 | 1931774 | Colbourn-Martirosyan-Trung-Walker |
| 7562 | 1936280 | Colbourn-Martirosyan-Trung-Walker |
| 7600 | 1939324 | Colbourn-Martirosyan-Trung-Walker |
| 7714 | 2080915 | Colbourn-Martirosyan-Trung-Walker |
| 7942 | 2085541 | Colbourn-Martirosyan-Trung-Walker |
| 8246 | 2092757 | Colbourn-Martirosyan-Trung-Walker |
| 8303 | 2095945 | Colbourn-Martirosyan-Trung-Walker |
| 8398 | 2097313 | Colbourn-Martirosyan-Trung-Walker |
| 8664 | 2103785 | Colbourn-Martirosyan-Trung-Walker |
| 8702 | 2182893 | Colbourn-Martirosyan-Trung-Walker |
| 9025 | 2191163 | Colbourn-Martirosyan-Trung-Walker |
| 9082 | 2191811 | Colbourn-Martirosyan-Trung-Walker |
| 9158 | 2193489 | Colbourn-Martirosyan-Trung-Walker |
| 9386 | 2201999 | Colbourn-Martirosyan-Trung-Walker |
| 9538 | 2202971 | Colbourn-Martirosyan-Trung-Walker |
| 9614 | 2204697 | Colbourn-Martirosyan-Trung-Walker |
| 9747 | 2209923 | Colbourn-Martirosyan-Trung-Walker |
| 9842 | 2210571 | Colbourn-Martirosyan-Trung-Walker |
| 9994 | 2214095 | Colbourn-Martirosyan-Trung-Walker |
| 10000 | 2219441 | Colbourn-Martirosyan-Trung-Walker |