Information on Result #598942
There is no digital (11, 32, 45)-net over F3, because extracting embedded orthogonal array would yield linear OA(332, 45, F3, 21) (dual of [45, 13, 22]-code), but
- construction Y1 [i] would yield
- linear OA(331, 37, F3, 21) (dual of [37, 6, 22]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- OA(313, 45, S3, 8), but
- discarding factors would yield OA(313, 41, S3, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 1 708963 > 313 [i]
- discarding factors would yield OA(313, 41, S3, 8), but
- linear OA(331, 37, F3, 21) (dual of [37, 6, 22]-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 (11, 33, 45)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (11, 34, 45)-net over F3 | [i] | ||