Information on Result #548598
There is no linear OA(3164, 189, F3, 108) (dual of [189, 25, 109]-code), because construction Y1 would yield
- linear OA(3163, 177, F3, 108) (dual of [177, 14, 109]-code), but
- construction Y1 [i] would yield
- linear OA(3162, 171, F3, 108) (dual of [171, 9, 109]-code), but
- construction Y1 [i] would yield
- linear OA(3161, 167, F3, 108) (dual of [167, 6, 109]-code), but
- residual code [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
- residual code [i] would yield linear OA(353, 58, F3, 36) (dual of [58, 5, 37]-code), but
- OA(39, 171, 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(3161, 167, F3, 108) (dual of [167, 6, 109]-code), but
- construction Y1 [i] would yield
- OA(314, 177, 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
- linear OA(3162, 171, F3, 108) (dual of [171, 9, 109]-code), but
- construction Y1 [i] would yield
- OA(325, 189, S3, 12), but
- discarding factors would yield OA(325, 148, S3, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 861032 991633 > 325 [i]
- discarding factors would yield OA(325, 148, S3, 12), 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(3165, 190, F3, 109) (dual of [190, 25, 110]-code) | [i] | Truncation | |
| 2 | No linear OA(3166, 191, F3, 110) (dual of [191, 25, 111]-code) | [i] | ||
| 3 | No linear OOA(3165, 189, F3, 2, 109) (dual of [(189, 2), 213, 110]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3166, 189, F3, 2, 110) (dual of [(189, 2), 212, 111]-NRT-code) | [i] | ||
| 5 | No linear OOA(3164, 189, F3, 2, 108) (dual of [(189, 2), 214, 109]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3164, 189, F3, 3, 108) (dual of [(189, 3), 403, 109]-NRT-code) | [i] | ||
| 7 | No linear OOA(3164, 189, F3, 4, 108) (dual of [(189, 4), 592, 109]-NRT-code) | [i] | ||
| 8 | No linear OOA(3164, 189, F3, 5, 108) (dual of [(189, 5), 781, 109]-NRT-code) | [i] | ||
| 9 | No digital (56, 164, 189)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |