Information on Result #598938
There is no digital (10, 28, 47)-net over F3, because extracting embedded orthogonal array would yield linear OA(328, 47, F3, 18) (dual of [47, 19, 19]-code), but
- construction Y1 [i] would yield
- linear OA(327, 35, F3, 18) (dual of [35, 8, 19]-code), but
- residual code [i] would yield linear OA(39, 16, F3, 6) (dual of [16, 7, 7]-code), but
- “vE2†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(39, 16, F3, 6) (dual of [16, 7, 7]-code), but
- linear OA(319, 47, F3, 12) (dual of [47, 28, 13]-code), but
- discarding factors / shortening the dual code would yield linear OA(319, 46, F3, 12) (dual of [46, 27, 13]-code), but
- residual code [i] would yield OA(37, 33, S3, 4), but
- the linear programming bound shows that M ≥ 64125 / 28 > 37 [i]
- residual code [i] would yield OA(37, 33, S3, 4), but
- discarding factors / shortening the dual code would yield linear OA(319, 46, F3, 12) (dual of [46, 27, 13]-code), but
- linear OA(327, 35, F3, 18) (dual of [35, 8, 19]-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 (10, 29, 47)-net over F3 | [i] | m-Reduction | |