Information on Result #547778
There is no linear OA(3132, 163, F3, 85) (dual of [163, 31, 86]-code), because construction Y1 would yield
- OA(3131, 147, S3, 85), but
- the linear programming bound shows that M ≥ 2 959964 272368 355385 131019 565631 322230 864774 663367 805086 508948 978796 443201 / 9282 754000 > 3131 [i]
- OA(331, 163, S3, 16), but
- discarding factors would yield OA(331, 136, S3, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 621 653656 785825 > 331 [i]
- discarding factors would yield OA(331, 136, 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(3132, 163, F3, 2, 85) (dual of [(163, 2), 194, 86]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3132, 163, F3, 3, 85) (dual of [(163, 3), 357, 86]-NRT-code) | [i] | ||
| 3 | No linear OOA(3132, 163, F3, 4, 85) (dual of [(163, 4), 520, 86]-NRT-code) | [i] | ||
| 4 | No linear OOA(3132, 163, F3, 5, 85) (dual of [(163, 5), 683, 86]-NRT-code) | [i] | ||
| 5 | No linear OA(3133, 201, F3, 85) (dual of [201, 68, 86]-code) | [i] | Construction Y1 (Bound) | |