Information on Result #547788
There is no linear OA(3138, 187, F3, 89) (dual of [187, 49, 90]-code), because construction Y1 would yield
- linear OA(3137, 161, F3, 89) (dual of [161, 24, 90]-code), but
- construction Y1 [i] would yield
- OA(3136, 149, S3, 89), but
- the linear programming bound shows that M ≥ 6 385896 362423 839893 456186 755923 270794 744764 572661 578917 513381 685836 804369 / 75 686875 > 3136 [i]
- OA(324, 161, S3, 12), but
- discarding factors would yield OA(324, 124, S3, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 293147 842993 > 324 [i]
- discarding factors would yield OA(324, 124, S3, 12), but
- OA(3136, 149, S3, 89), but
- construction Y1 [i] would yield
- OA(349, 187, S3, 26), but
- discarding factors would yield OA(349, 184, S3, 26), but
- the Rao or (dual) Hamming bound shows that M ≥ 245469 510905 440390 144353 > 349 [i]
- discarding factors would yield OA(349, 184, 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 OA(3139, 188, F3, 90) (dual of [188, 49, 91]-code) | [i] | Truncation | |
| 2 | No linear OOA(3139, 187, F3, 2, 90) (dual of [(187, 2), 235, 91]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(3138, 187, F3, 2, 89) (dual of [(187, 2), 236, 90]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(3138, 187, F3, 3, 89) (dual of [(187, 3), 423, 90]-NRT-code) | [i] | ||
| 5 | No linear OOA(3138, 187, F3, 4, 89) (dual of [(187, 4), 610, 90]-NRT-code) | [i] | ||
| 6 | No linear OOA(3138, 187, F3, 5, 89) (dual of [(187, 5), 797, 90]-NRT-code) | [i] | ||
| 7 | No digital (49, 138, 187)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |