Information on Result #548587
There is no linear OA(342, 53, F3, 28) (dual of [53, 11, 29]-code), because construction Y1 would yield
- linear OA(341, 47, F3, 28) (dual of [47, 6, 29]-code), but
- OA(311, 53, S3, 6), but
- discarding factors would yield OA(311, 52, S3, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 182209 > 311 [i]
- discarding factors would yield OA(311, 52, S3, 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(343, 54, F3, 29) (dual of [54, 11, 30]-code) | [i] | Truncation | |
| 2 | No linear OOA(343, 53, F3, 2, 29) (dual of [(53, 2), 63, 30]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(342, 53, F3, 2, 28) (dual of [(53, 2), 64, 29]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(342, 53, F3, 3, 28) (dual of [(53, 3), 117, 29]-NRT-code) | [i] | ||
| 5 | No linear OOA(342, 53, F3, 4, 28) (dual of [(53, 4), 170, 29]-NRT-code) | [i] | ||
| 6 | No linear OOA(342, 53, F3, 5, 28) (dual of [(53, 5), 223, 29]-NRT-code) | [i] | ||
| 7 | No digital (14, 42, 53)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |