Information on Result #547772
There is no linear OA(3128, 176, F3, 81) (dual of [176, 48, 82]-code), because construction Y1 would yield
- OA(3127, 150, S3, 81), but
- the linear programming bound shows that M ≥ 34 591649 218027 645930 654651 997419 100907 498551 201171 263936 373038 687154 245563 / 8 746966 630402 > 3127 [i]
- OA(348, 176, S3, 26), but
- discarding factors would yield OA(348, 170, S3, 26), but
- the Rao or (dual) Hamming bound shows that M ≥ 84876 685847 451322 200873 > 348 [i]
- discarding factors would yield OA(348, 170, S3, 26), 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(3128, 176, F3, 2, 81) (dual of [(176, 2), 224, 82]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3128, 176, F3, 3, 81) (dual of [(176, 3), 400, 82]-NRT-code) | [i] | ||
| 3 | No linear OOA(3128, 176, F3, 4, 81) (dual of [(176, 4), 576, 82]-NRT-code) | [i] | ||
| 4 | No linear OOA(3128, 176, F3, 5, 81) (dual of [(176, 5), 752, 82]-NRT-code) | [i] | ||
| 5 | No digital (47, 128, 176)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |