Information on Result #598807
There is no digital (96, 180, 225)-net over F2, because extracting embedded orthogonal array would yield linear OA(2180, 225, F2, 84) (dual of [225, 45, 85]-code), but
- construction Y1 [i] would yield
- linear OA(2179, 209, F2, 84) (dual of [209, 30, 85]-code), but
- adding a parity check bit [i] would yield linear OA(2180, 210, F2, 85) (dual of [210, 30, 86]-code), but
- OA(245, 225, S2, 16), but
- discarding factors would yield OA(245, 189, S2, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 36 338770 420561 > 245 [i]
- discarding factors would yield OA(245, 189, S2, 16), but
- linear OA(2179, 209, F2, 84) (dual of [209, 30, 85]-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 (96, 181, 225)-net over F2 | [i] | m-Reduction | |