| k | N | Source |
| 6 | 400 | orthogonal array |
| 7 | 432 | orthogonal array fuse postop NCK |
| 8 | 513 | Derive from strength 3 |
| 24 | 514 | orthogonal array fuse fuse fuse postop NCK |
| 25 | 517 | projection (Colbourn) fuse fuse postop NCK |
| 26 | 520 | projection (Colbourn) fuse postop NCK |
| 27 | 523 | projection (Colbourn) postop NCK |
| 28 | 593 | projection (Colbourn) fuse fuse fuse postop NCK |
| 29 | 596 | projection (Colbourn) fuse fuse postop NCK |
| 30 | 600 | projection (Colbourn) fuse postop NCK |
| 31 | 603 | projection (Colbourn) postop NCK |
| 32 | 668 | projection (Colbourn) fuse fuse fuse postop NCK |
| 33 | 673 | projection (Colbourn) fuse fuse postop NCK |
| 34 | 675 | projection (Colbourn) fuse postop NCK |
| 35 | 678 | projection (Colbourn) postop NCK |
| 37 | 737 | projection (Colbourn) fuse fuse postop NCK |
| 39 | 742 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 40 | 761 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 41 | 780 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 42 | 799 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 43 | 818 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 44 | 837 | group 1-rotational (Meagher-Stevens, Colbourn) |
| 48 | 856 | CMMSSY 2.2 |
| 49 | 863 | CMMSSY 2.2 |
| 144 | 894 | CMMSSY 2.2 |
| 150 | 897 | CMMSSY 2.2 |
| 156 | 900 | CMMSSY 2.2 |
| 162 | 903 | CMMSSY 2.2 |
| 163 | 934 | CMMSSY 2.2 |
| 189 | 938 | CMMSSY 2.2 |
| 554 | 1016 | CMMSSY 2.2 |
| 577 | 1019 | CMMSSY 2.2 |
| 648 | 1020 | CMMSSY 2.2 |
| 675 | 1023 | CMMSSY 2.2 |
| 702 | 1026 | CMMSSY 2.2 |
| 729 | 1029 | CMMSSY 2.2 |
| 756 | 1099 | CMMSSY 2.2 |
| 783 | 1102 | CMMSSY 2.2 |
| 810 | 1106 | CMMSSY 2.2 |
| 837 | 1109 | CMMSSY 2.2 |
| 864 | 1174 | CMMSSY 2.2 |
| 891 | 1179 | CMMSSY 2.2 |
| 918 | 1181 | CMMSSY 2.2 |
| 945 | 1184 | CMMSSY 2.2 |
| 961 | 1203 | CMMSSY 2.2 |
| 990 | 1242 | CMMSSY 2.2 |
| 999 | 1243 | CMMSSY 2.2 |
| 1028 | 1245 | CMMSSY 2.2 |
| 1053 | 1248 | CMMSSY 2.2 |
| 1055 | 1264 | CMMSSY 2.2 |
| 1080 | 1267 | CMMSSY 2.2 |
| 1085 | 1278 | CMMSSY 2.2 |
| 1107 | 1286 | CMMSSY 2.2 |
| 1109 | 1302 | CMMSSY 2.2 |
| 1134 | 1305 | CMMSSY 2.2 |
| 1136 | 1321 | CMMSSY 2.2 |
| 1142 | 1322 | CMMSSY 2.2 |
| 1161 | 1324 | CMMSSY 2.2 |
| 1180 | 1325 | CMMSSY 2.2 |
| 1209 | 1342 | CMMSSY 2.2 |
| 1211 | 1344 | CMMSSY 2.2 |
| 1323 | 1350 | CMMSSY 2.2 |
| 2884 | 1388 | CMMSSY 2.2 |
| 3004 | 1391 | CMMSSY 2.2 |
| 3124 | 1394 | CMMSSY 2.2 |
| 3324 | 1396 | CMMSSY 2.2 |
| 3462 | 1399 | CMMSSY 2.2 |
| 3888 | 1400 | CMMSSY 2.2 |
| 4050 | 1403 | CMMSSY 2.2 |
| 4212 | 1406 | CMMSSY 2.2 |
| 4374 | 1409 | CMMSSY 2.2 |
| 4536 | 1432 | CMMSSY 2.2 |
| 4725 | 1435 | CMMSSY 2.2 |
| 4914 | 1438 | CMMSSY 2.2 |
| 5103 | 1441 | CMMSSY 2.2 |
| 5292 | 1511 | CMMSSY 2.2 |
| 15552 | 1514 | CMMSSY 2.2 |
| 16200 | 1517 | CMMSSY 2.2 |
| 16875 | 1520 | CMMSSY 2.2 |
| 17550 | 1523 | CMMSSY 2.2 |
| 18252 | 1526 | CMMSSY 2.2 |
| 18954 | 1529 | CMMSSY 2.2 |
| 19683 | 1532 | CMMSSY 2.2 |
| 20000 | 1602 | CMMSSY 2.2 |