Information on Result #599900
There is no digital (2, 32, 66)-net over F16, because extracting embedded orthogonal array would yield linear OA(1632, 66, F16, 30) (dual of [66, 34, 31]-code), but
- construction Y1 [i] would yield
- linear OA(1631, 34, F16, 30) (dual of [34, 3, 31]-code), but
- linear OA(1634, 66, F16, 32) (dual of [66, 32, 33]-code), but
- discarding factors / shortening the dual code would yield linear OA(1634, 51, F16, 32) (dual of [51, 17, 33]-code), but
- residual code [i] would yield OA(162, 18, S16, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 271 > 162 [i]
- residual code [i] would yield OA(162, 18, S16, 2), but
- discarding factors / shortening the dual code would yield linear OA(1634, 51, F16, 32) (dual of [51, 17, 33]-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 (2, 33, 66)-net over F16 | [i] | m-Reduction | |