Information on Result #547741
There is no linear OA(341, 55, F3, 27) (dual of [55, 14, 28]-code), because construction Y1 would yield
- linear OA(340, 47, F3, 27) (dual of [47, 7, 28]-code), but
- construction Y1 [i] would yield
- linear OA(339, 43, F3, 27) (dual of [43, 4, 28]-code), but
- OA(37, 47, S3, 4), but
- discarding factors would yield OA(37, 34, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 2313 > 37 [i]
- discarding factors would yield OA(37, 34, S3, 4), but
- construction Y1 [i] would yield
- OA(314, 55, S3, 8), but
- discarding factors would yield OA(314, 53, S3, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 878227 > 314 [i]
- discarding factors would yield OA(314, 53, S3, 8), 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(341, 55, F3, 2, 27) (dual of [(55, 2), 69, 28]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(341, 55, F3, 3, 27) (dual of [(55, 3), 124, 28]-NRT-code) | [i] | ||
| 3 | No linear OOA(341, 55, F3, 4, 27) (dual of [(55, 4), 179, 28]-NRT-code) | [i] | ||
| 4 | No linear OOA(341, 55, F3, 5, 27) (dual of [(55, 5), 234, 28]-NRT-code) | [i] | ||
| 5 | No digital (14, 41, 55)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |