Information on Result #547782
There is no linear OA(3134, 166, F3, 86) (dual of [166, 32, 87]-code), because construction Y1 would yield
- OA(3133, 150, S3, 86), but
- the linear programming bound shows that M ≥ 10206 967808 467913 747808 389212 583004 511164 705253 854573 732746 285224 754829 / 2 832691 > 3133 [i]
- OA(332, 166, S3, 16), but
- discarding factors would yield OA(332, 156, S3, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 1906 607562 901809 > 332 [i]
- discarding factors would yield OA(332, 156, S3, 16), 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(3134, 166, F3, 2, 86) (dual of [(166, 2), 198, 87]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3134, 166, F3, 3, 86) (dual of [(166, 3), 364, 87]-NRT-code) | [i] | ||
| 3 | No linear OOA(3134, 166, F3, 4, 86) (dual of [(166, 4), 530, 87]-NRT-code) | [i] | ||
| 4 | No linear OOA(3134, 166, F3, 5, 86) (dual of [(166, 5), 696, 87]-NRT-code) | [i] | ||
| 5 | No digital (48, 134, 166)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(3135, 204, F3, 86) (dual of [204, 69, 87]-code) | [i] | Construction Y1 (Bound) | |