Information on Result #599027
There is no digital (49, 143, 168)-net over F3, because extracting embedded orthogonal array would yield linear OA(3143, 168, F3, 94) (dual of [168, 25, 95]-code), but
- construction Y1 [i] would yield
- linear OA(3142, 156, F3, 94) (dual of [156, 14, 95]-code), but
- construction Y1 [i] would yield
- OA(3141, 150, S3, 94), but
- the linear programming bound shows that M ≥ 2 507699 731904 749483 156305 303283 721699 486095 458197 011266 969583 191489 627021 / 107749 > 3141 [i]
- OA(314, 156, S3, 6), but
- discarding factors would yield OA(314, 154, S3, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 822665 > 314 [i]
- discarding factors would yield OA(314, 154, S3, 6), but
- OA(3141, 150, S3, 94), but
- construction Y1 [i] would yield
- OA(325, 168, S3, 12), but
- discarding factors would yield OA(325, 148, S3, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 861032 991633 > 325 [i]
- discarding factors would yield OA(325, 148, S3, 12), but
- linear OA(3142, 156, F3, 94) (dual of [156, 14, 95]-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, 144, 168)-net over F3 | [i] | m-Reduction | |