Information on Result #599024
There is no digital (49, 138, 187)-net over F3, because extracting embedded orthogonal array would yield linear OA(3138, 187, F3, 89) (dual of [187, 49, 90]-code), but
- construction Y1 [i] 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
- linear OA(3137, 161, F3, 89) (dual of [161, 24, 90]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (49, 139, 187)-net over F3 | [i] | m-Reduction | |