Information on Result #547142
There is no linear OA(4148, 224, F4, 108) (dual of [224, 76, 109]-code), because residual code would yield OA(440, 115, S4, 27), but
- the linear programming bound shows that M ≥ 929 557766 490609 787836 487564 000967 310274 723840 000000 / 708 347236 523196 849504 526399 > 440 [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(4149, 225, F4, 109) (dual of [225, 76, 110]-code) | [i] | Truncation | |
| 2 | No linear OA(4150, 226, F4, 110) (dual of [226, 76, 111]-code) | [i] | ||
| 3 | No linear OA(4151, 227, F4, 111) (dual of [227, 76, 112]-code) | [i] | ||
| 4 | No linear OOA(4149, 224, F4, 2, 109) (dual of [(224, 2), 299, 110]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4150, 224, F4, 2, 110) (dual of [(224, 2), 298, 111]-NRT-code) | [i] | ||
| 6 | No linear OOA(4151, 224, F4, 2, 111) (dual of [(224, 2), 297, 112]-NRT-code) | [i] | ||
| 7 | No linear OOA(4148, 224, F4, 2, 108) (dual of [(224, 2), 300, 109]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4148, 224, F4, 3, 108) (dual of [(224, 3), 524, 109]-NRT-code) | [i] | ||
| 9 | No digital (40, 148, 224)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |