Information on Result #599011
There is no digital (47, 131, 163)-net over F3, because extracting embedded orthogonal array would yield linear OA(3131, 163, F3, 84) (dual of [163, 32, 85]-code), but
- construction Y1 [i] would yield
- OA(3130, 147, S3, 84), but
- the linear programming bound shows that M ≥ 610951 874237 245179 799757 396293 504258 972145 948730 720728 290459 967541 402306 / 4917 657235 > 3130 [i]
- OA(332, 163, S3, 16), but
- discarding factors would yield OA(332, 156, S3, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 1906 607562 901809 > 332 [i]
- discarding factors would yield OA(332, 156, S3, 16), but
- OA(3130, 147, S3, 84), 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 (47, 132, 163)-net over F3 | [i] | m-Reduction | |