Information on Result #548581
There is no linear OA(328, 47, F3, 18) (dual of [47, 19, 19]-code), because construction Y1 would yield
- linear OA(327, 35, F3, 18) (dual of [35, 8, 19]-code), but
- residual code [i] would yield linear OA(39, 16, F3, 6) (dual of [16, 7, 7]-code), but
- “vE2†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(39, 16, F3, 6) (dual of [16, 7, 7]-code), but
- linear OA(319, 47, F3, 12) (dual of [47, 28, 13]-code), but
- discarding factors / shortening the dual code would yield linear OA(319, 46, F3, 12) (dual of [46, 27, 13]-code), but
- residual code [i] would yield OA(37, 33, S3, 4), but
- the linear programming bound shows that M ≥ 64125 / 28 > 37 [i]
- residual code [i] would yield OA(37, 33, S3, 4), but
- discarding factors / shortening the dual code would yield linear OA(319, 46, F3, 12) (dual of [46, 27, 13]-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 OA(329, 48, F3, 19) (dual of [48, 19, 20]-code) | [i] | Truncation | |
| 2 | No linear OOA(329, 47, F3, 2, 19) (dual of [(47, 2), 65, 20]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(328, 47, F3, 2, 18) (dual of [(47, 2), 66, 19]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(328, 47, F3, 3, 18) (dual of [(47, 3), 113, 19]-NRT-code) | [i] | ||
| 5 | No linear OOA(328, 47, F3, 4, 18) (dual of [(47, 4), 160, 19]-NRT-code) | [i] | ||
| 6 | No linear OOA(328, 47, F3, 5, 18) (dual of [(47, 5), 207, 19]-NRT-code) | [i] | ||
| 7 | No digital (10, 28, 47)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |