Information on Result #547316
There is no linear OA(4211, 261, F4, 156) (dual of [261, 50, 157]-code), because residual code would yield OA(455, 104, S4, 39), but
- the linear programming bound shows that M ≥ 7 723473 632829 389285 976355 541453 254660 289881 978452 313500 994274 223551 712140 212225 490113 864437 287145 948134 332311 964905 619217 330530 016843 066600 998037 356544 / 5779 127016 748909 094986 667927 666304 897550 201537 672172 684327 799525 226094 950381 356180 131377 653225 244035 788465 702327 464125 > 455 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(4212, 262, F4, 157) (dual of [262, 50, 158]-code) | [i] | Truncation | |
| 2 | No linear OA(4213, 263, F4, 158) (dual of [263, 50, 159]-code) | [i] | ||
| 3 | No linear OA(4214, 264, F4, 159) (dual of [264, 50, 160]-code) | [i] | ||
| 4 | No linear OOA(4212, 261, F4, 2, 157) (dual of [(261, 2), 310, 158]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4213, 261, F4, 2, 158) (dual of [(261, 2), 309, 159]-NRT-code) | [i] | ||
| 6 | No linear OOA(4214, 261, F4, 2, 159) (dual of [(261, 2), 308, 160]-NRT-code) | [i] | ||
| 7 | No linear OOA(4211, 261, F4, 2, 156) (dual of [(261, 2), 311, 157]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4211, 261, F4, 3, 156) (dual of [(261, 3), 572, 157]-NRT-code) | [i] | ||
| 9 | No digital (55, 211, 261)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |