Information on Result #547314
There is no linear OA(4209, 230, F4, 156) (dual of [230, 21, 157]-code), because residual code would yield OA(453, 73, S4, 39), but
- the linear programming bound shows that M ≥ 498171 059023 261286 907602 843617 753170 968576 / 5511 193875 > 453 [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(4210, 231, F4, 157) (dual of [231, 21, 158]-code) | [i] | Truncation | |
| 2 | No linear OA(4211, 232, F4, 158) (dual of [232, 21, 159]-code) | [i] | ||
| 3 | No linear OA(4212, 233, F4, 159) (dual of [233, 21, 160]-code) | [i] | ||
| 4 | No linear OOA(4210, 230, F4, 2, 157) (dual of [(230, 2), 250, 158]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4211, 230, F4, 2, 158) (dual of [(230, 2), 249, 159]-NRT-code) | [i] | ||
| 6 | No linear OOA(4212, 230, F4, 2, 159) (dual of [(230, 2), 248, 160]-NRT-code) | [i] | ||
| 7 | No linear OOA(4209, 230, F4, 2, 156) (dual of [(230, 2), 251, 157]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4209, 230, F4, 3, 156) (dual of [(230, 3), 481, 157]-NRT-code) | [i] | ||
| 9 | No digital (53, 209, 230)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |