Information on Result #548592
There is no linear OA(368, 80, F3, 45) (dual of [80, 12, 46]-code), because construction Y1 would yield
- linear OA(367, 74, F3, 45) (dual of [74, 7, 46]-code), but
- residual code [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- “HHM†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- OA(312, 80, S3, 6), but
- discarding factors would yield OA(312, 75, S3, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 551451 > 312 [i]
- discarding factors would yield OA(312, 75, 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(368, 80, F3, 2, 45) (dual of [(80, 2), 92, 46]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(368, 80, F3, 3, 45) (dual of [(80, 3), 172, 46]-NRT-code) | [i] | ||
| 3 | No linear OOA(368, 80, F3, 4, 45) (dual of [(80, 4), 252, 46]-NRT-code) | [i] | ||
| 4 | No linear OOA(368, 80, F3, 5, 45) (dual of [(80, 5), 332, 46]-NRT-code) | [i] | ||
| 5 | No digital (23, 68, 80)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |