Information on Result #547793
There is no linear OA(3143, 168, F3, 94) (dual of [168, 25, 95]-code), because construction Y1 would yield
- linear OA(3142, 156, F3, 94) (dual of [156, 14, 95]-code), but
- construction Y1 [i] would yield
- OA(3141, 150, S3, 94), but
- the linear programming bound shows that M ≥ 2 507699 731904 749483 156305 303283 721699 486095 458197 011266 969583 191489 627021 / 107749 > 3141 [i]
- OA(314, 156, 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
- OA(3141, 150, S3, 94), but
- construction Y1 [i] would yield
- OA(325, 168, 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(3144, 169, F3, 95) (dual of [169, 25, 96]-code) | [i] | Truncation | |
| 2 | No linear OOA(3144, 168, F3, 2, 95) (dual of [(168, 2), 192, 96]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(3143, 168, F3, 2, 94) (dual of [(168, 2), 193, 95]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(3143, 168, F3, 3, 94) (dual of [(168, 3), 361, 95]-NRT-code) | [i] | ||
| 5 | No linear OOA(3143, 168, F3, 4, 94) (dual of [(168, 4), 529, 95]-NRT-code) | [i] | ||
| 6 | No linear OOA(3143, 168, F3, 5, 94) (dual of [(168, 5), 697, 95]-NRT-code) | [i] | ||
| 7 | No digital (49, 143, 168)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |