Information on Result #547773
There is no linear OA(3129, 171, F3, 82) (dual of [171, 42, 83]-code), because construction Y1 would yield
- OA(3128, 149, S3, 82), but
- the linear programming bound shows that M ≥ 33 761969 841965 313899 084622 936677 465357 394104 583425 843880 075496 568722 581771 / 1 948280 920300 > 3128 [i]
- OA(342, 171, S3, 22), but
- discarding factors would yield OA(342, 168, S3, 22), but
- the Rao or (dual) Hamming bound shows that M ≥ 114 464714 711551 910433 > 342 [i]
- discarding factors would yield OA(342, 168, S3, 22), 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(3129, 171, F3, 2, 82) (dual of [(171, 2), 213, 83]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3129, 171, F3, 3, 82) (dual of [(171, 3), 384, 83]-NRT-code) | [i] | ||
| 3 | No linear OOA(3129, 171, F3, 4, 82) (dual of [(171, 4), 555, 83]-NRT-code) | [i] | ||
| 4 | No linear OOA(3129, 171, F3, 5, 82) (dual of [(171, 5), 726, 83]-NRT-code) | [i] | ||
| 5 | No digital (47, 129, 171)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |