Information on Result #548588
There is no linear OA(345, 56, F3, 30) (dual of [56, 11, 31]-code), because construction Y1 would yield
- linear OA(344, 50, F3, 30) (dual of [50, 6, 31]-code), but
- “HJL†bound on codes from Brouwer’s database [i]
- OA(311, 56, 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 OOA(345, 56, F3, 2, 30) (dual of [(56, 2), 67, 31]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(345, 56, F3, 3, 30) (dual of [(56, 3), 123, 31]-NRT-code) | [i] | ||
| 3 | No linear OOA(345, 56, F3, 4, 30) (dual of [(56, 4), 179, 31]-NRT-code) | [i] | ||
| 4 | No linear OOA(345, 56, F3, 5, 30) (dual of [(56, 5), 235, 31]-NRT-code) | [i] | ||
| 5 | No digital (15, 45, 56)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |