Information on Result #547776
There is no linear OA(3131, 163, F3, 84) (dual of [163, 32, 85]-code), because construction Y1 would yield
- OA(3130, 147, S3, 84), but
- the linear programming bound shows that M ≥ 610951 874237 245179 799757 396293 504258 972145 948730 720728 290459 967541 402306 / 4917 657235 > 3130 [i]
- OA(332, 163, 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(3131, 163, F3, 2, 84) (dual of [(163, 2), 195, 85]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3131, 163, F3, 3, 84) (dual of [(163, 3), 358, 85]-NRT-code) | [i] | ||
| 3 | No linear OOA(3131, 163, F3, 4, 84) (dual of [(163, 4), 521, 85]-NRT-code) | [i] | ||
| 4 | No linear OOA(3131, 163, F3, 5, 84) (dual of [(163, 5), 684, 85]-NRT-code) | [i] | ||
| 5 | No digital (47, 131, 163)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 6 | No linear OA(3132, 202, F3, 84) (dual of [202, 70, 85]-code) | [i] | Construction Y1 (Bound) | |