Information on Result #600002
There is no digital (2, 64, 130)-net over F32, because extracting embedded orthogonal array would yield linear OA(3264, 130, F32, 62) (dual of [130, 66, 63]-code), but
- construction Y1 [i] would yield
- linear OA(3263, 66, F32, 62) (dual of [66, 3, 63]-code), but
- linear OA(3266, 130, F32, 64) (dual of [130, 64, 65]-code), but
- discarding factors / shortening the dual code would yield linear OA(3266, 99, F32, 64) (dual of [99, 33, 65]-code), but
- residual code [i] would yield OA(322, 34, S32, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 1055 > 322 [i]
- residual code [i] would yield OA(322, 34, S32, 2), but
- discarding factors / shortening the dual code would yield linear OA(3266, 99, F32, 64) (dual of [99, 33, 65]-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, 65, 130)-net over F32 | [i] | m-Reduction | |