Information on Result #547324
There is no linear OA(4219, 390, F4, 156) (dual of [390, 171, 157]-code), because residual code would yield OA(463, 233, S4, 39), but
- the linear programming bound shows that M ≥ 2 394144 335707 471520 884224 011051 775831 492539 148504 246999 784192 681791 545828 966400 000000 / 26753 789254 137656 696530 296222 884590 520869 895903 > 463 [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(4220, 391, F4, 157) (dual of [391, 171, 158]-code) | [i] | Truncation | |
| 2 | No linear OA(4221, 392, F4, 158) (dual of [392, 171, 159]-code) | [i] | ||
| 3 | No linear OA(4222, 393, F4, 159) (dual of [393, 171, 160]-code) | [i] | ||
| 4 | No linear OOA(4220, 390, F4, 2, 157) (dual of [(390, 2), 560, 158]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4221, 390, F4, 2, 158) (dual of [(390, 2), 559, 159]-NRT-code) | [i] | ||
| 6 | No linear OOA(4222, 390, F4, 2, 159) (dual of [(390, 2), 558, 160]-NRT-code) | [i] | ||
| 7 | No linear OOA(4219, 390, F4, 2, 156) (dual of [(390, 2), 561, 157]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4219, 390, F4, 3, 156) (dual of [(390, 3), 951, 157]-NRT-code) | [i] | ||
| 9 | No digital (63, 219, 390)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |