Information on Result #599019
There is no digital (48, 142, 156)-net over F3, because extracting embedded orthogonal array 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
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 (48, 143, 156)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (48, 144, 156)-net over F3 | [i] | ||
| 3 | No digital (48, 145, 156)-net over F3 | [i] | ||
| 4 | No digital (48, 146, 156)-net over F3 | [i] | ||