Information on Result #547790
There is no linear OA(3140, 182, F3, 91) (dual of [182, 42, 92]-code), because construction Y1 would yield
- linear OA(3139, 160, F3, 91) (dual of [160, 21, 92]-code), but
- construction Y1 [i] would yield
- OA(3138, 150, S3, 91), but
- the linear programming bound shows that M ≥ 13 106423 371120 876472 986931 421169 566720 811359 868949 528224 695915 065174 686944 / 17 599301 > 3138 [i]
- OA(321, 160, S3, 10), but
- discarding factors would yield OA(321, 133, S3, 10), but
- the Rao or (dual) Hamming bound shows that M ≥ 10487 287539 > 321 [i]
- discarding factors would yield OA(321, 133, S3, 10), but
- OA(3138, 150, S3, 91), but
- construction Y1 [i] would yield
- OA(342, 182, 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 OA(3141, 183, F3, 92) (dual of [183, 42, 93]-code) | [i] | Truncation | |
| 2 | No linear OOA(3141, 182, F3, 2, 92) (dual of [(182, 2), 223, 93]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(3140, 182, F3, 2, 91) (dual of [(182, 2), 224, 92]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(3140, 182, F3, 3, 91) (dual of [(182, 3), 406, 92]-NRT-code) | [i] | ||
| 5 | No linear OOA(3140, 182, F3, 4, 91) (dual of [(182, 4), 588, 92]-NRT-code) | [i] | ||
| 6 | No linear OOA(3140, 182, F3, 5, 91) (dual of [(182, 5), 770, 92]-NRT-code) | [i] | ||
| 7 | No digital (49, 140, 182)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |