Information on Result #548586
There is no linear OA(337, 62, F3, 24) (dual of [62, 25, 25]-code), because construction Y1 would yield
- linear OA(336, 46, F3, 24) (dual of [46, 10, 25]-code), but
- construction Y1 [i] would yield
- linear OA(335, 40, F3, 24) (dual of [40, 5, 25]-code), but
- “vE1†bound on codes from Brouwer’s database [i]
- OA(310, 46, S3, 6), but
- discarding factors would yield OA(310, 36, S3, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 59713 > 310 [i]
- discarding factors would yield OA(310, 36, S3, 6), but
- linear OA(335, 40, F3, 24) (dual of [40, 5, 25]-code), but
- construction Y1 [i] would yield
- OA(325, 62, S3, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 932661 812025 > 325 [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 OOA(337, 62, F3, 2, 24) (dual of [(62, 2), 87, 25]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(337, 62, F3, 3, 24) (dual of [(62, 3), 149, 25]-NRT-code) | [i] | ||
| 3 | No linear OOA(337, 62, F3, 4, 24) (dual of [(62, 4), 211, 25]-NRT-code) | [i] | ||
| 4 | No linear OOA(337, 62, F3, 5, 24) (dual of [(62, 5), 273, 25]-NRT-code) | [i] | ||
| 5 | No digital (13, 37, 62)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |