Information on Result #599103
There is no digital (59, 176, 190)-net over F3, because extracting embedded orthogonal array would yield linear OA(3176, 190, F3, 117) (dual of [190, 14, 118]-code), but
- construction Y1 [i] would yield
- linear OA(3175, 184, F3, 117) (dual of [184, 9, 118]-code), but
- construction Y1 [i] would yield
- linear OA(3174, 180, F3, 117) (dual of [180, 6, 118]-code), but
- residual code [i] would yield linear OA(357, 62, F3, 39) (dual of [62, 5, 40]-code), but
- residual code [i] would yield linear OA(318, 22, F3, 13) (dual of [22, 4, 14]-code), but
- 1 times truncation [i] would yield linear OA(317, 21, F3, 12) (dual of [21, 4, 13]-code), but
- residual code [i] would yield linear OA(318, 22, F3, 13) (dual of [22, 4, 14]-code), but
- residual code [i] would yield linear OA(357, 62, F3, 39) (dual of [62, 5, 40]-code), but
- OA(39, 184, 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(3174, 180, F3, 117) (dual of [180, 6, 118]-code), but
- construction Y1 [i] would yield
- OA(314, 190, 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(3175, 184, F3, 117) (dual of [184, 9, 118]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (59, 177, 190)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (59, 178, 190)-net over F3 | [i] | ||