Information on Result #548574
There is no linear OA(311, 27, F3, 7) (dual of [27, 16, 8]-code), because construction Y1 would yield
- linear OA(310, 16, F3, 7) (dual of [16, 6, 8]-code), but
- “vE2†bound on codes from Brouwer’s database [i]
- linear OA(316, 27, F3, 11) (dual of [27, 11, 12]-code), but
- discarding factors / shortening the dual code would yield linear OA(316, 24, F3, 11) (dual of [24, 8, 12]-code), 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(311, 27, F3, 2, 7) (dual of [(27, 2), 43, 8]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(311, 27, F3, 3, 7) (dual of [(27, 3), 70, 8]-NRT-code) | [i] | ||
| 3 | No linear OOA(311, 27, F3, 4, 7) (dual of [(27, 4), 97, 8]-NRT-code) | [i] | ||
| 4 | No linear OOA(311, 27, F3, 5, 7) (dual of [(27, 5), 124, 8]-NRT-code) | [i] | ||
| 5 | No digital (4, 11, 27)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |