Information on Result #548600
There is no linear OA(3167, 181, F3, 111) (dual of [181, 14, 112]-code), because construction Y1 would yield
- linear OA(3166, 175, F3, 111) (dual of [175, 9, 112]-code), but
- construction Y1 [i] would yield
- linear OA(3165, 171, F3, 111) (dual of [171, 6, 112]-code), but
- residual code [i] would yield linear OA(354, 59, F3, 37) (dual of [59, 5, 38]-code), but
- 1 times truncation [i] would yield linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- residual code [i] would yield linear OA(317, 21, F3, 12) (dual of [21, 4, 13]-code), but
- 1 times truncation [i] would yield linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- residual code [i] would yield linear OA(354, 59, F3, 37) (dual of [59, 5, 38]-code), but
- OA(39, 175, S3, 4), but
- discarding factors would yield OA(39, 100, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 20001 > 39 [i]
- discarding factors would yield OA(39, 100, S3, 4), but
- linear OA(3165, 171, F3, 111) (dual of [171, 6, 112]-code), but
- construction Y1 [i] would yield
- OA(314, 181, S3, 6), but
- discarding factors would yield OA(314, 154, S3, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 822665 > 314 [i]
- discarding factors would yield OA(314, 154, 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 OA(3168, 182, F3, 112) (dual of [182, 14, 113]-code) | [i] | Truncation | |
| 2 | No linear OA(3169, 183, F3, 113) (dual of [183, 14, 114]-code) | [i] | ||
| 3 | No linear OOA(3168, 181, F3, 2, 112) (dual of [(181, 2), 194, 113]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3169, 181, F3, 2, 113) (dual of [(181, 2), 193, 114]-NRT-code) | [i] | ||
| 5 | No linear OOA(3167, 181, F3, 2, 111) (dual of [(181, 2), 195, 112]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3167, 181, F3, 3, 111) (dual of [(181, 3), 376, 112]-NRT-code) | [i] | ||
| 7 | No linear OOA(3167, 181, F3, 4, 111) (dual of [(181, 4), 557, 112]-NRT-code) | [i] | ||
| 8 | No linear OOA(3167, 181, F3, 5, 111) (dual of [(181, 5), 738, 112]-NRT-code) | [i] | ||
| 9 | No digital (56, 167, 181)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |