Information on Result #547893
There is no linear OA(4176, 187, F4, 132) (dual of [187, 11, 133]-code), because construction Y1 would yield
- linear OA(4175, 181, F4, 132) (dual of [181, 6, 133]-code), but
- construction Y1 [i] would yield
- linear OA(4174, 178, F4, 132) (dual of [178, 4, 133]-code), but
- linear OA(46, 181, F4, 3) (dual of [181, 175, 4]-code or 181-cap in PG(5,4)), but
- construction Y1 [i] would yield
- OA(411, 187, S4, 6), but
- discarding factors would yield OA(411, 99, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 278880 > 411 [i]
- discarding factors would yield OA(411, 99, S4, 6), but
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(4177, 188, F4, 133) (dual of [188, 11, 134]-code) | [i] | Truncation | |
| 2 | No linear OA(4178, 189, F4, 134) (dual of [189, 11, 135]-code) | [i] | ||
| 3 | No linear OA(4179, 190, F4, 135) (dual of [190, 11, 136]-code) | [i] | ||
| 4 | No linear OOA(4177, 187, F4, 2, 133) (dual of [(187, 2), 197, 134]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4178, 187, F4, 2, 134) (dual of [(187, 2), 196, 135]-NRT-code) | [i] | ||
| 6 | No linear OOA(4179, 187, F4, 2, 135) (dual of [(187, 2), 195, 136]-NRT-code) | [i] | ||
| 7 | No linear OOA(4176, 187, F4, 2, 132) (dual of [(187, 2), 198, 133]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4176, 187, F4, 3, 132) (dual of [(187, 3), 385, 133]-NRT-code) | [i] | ||
| 9 | No digital (44, 176, 187)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(4177, 199, F4, 132) (dual of [199, 22, 133]-code) | [i] | Construction Y1 (Bound) | |