Information on Result #598724
There is no digital (81, 153, 193)-net over F2, because extracting embedded orthogonal array would yield linear OA(2153, 193, F2, 72) (dual of [193, 40, 73]-code), but
- construction Y1 [i] would yield
- linear OA(2152, 179, F2, 72) (dual of [179, 27, 73]-code), but
- adding a parity check bit [i] would yield linear OA(2153, 180, F2, 73) (dual of [180, 27, 74]-code), but
- OA(240, 193, S2, 14), but
- discarding factors would yield OA(240, 180, S2, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 1 124371 299892 > 240 [i]
- discarding factors would yield OA(240, 180, S2, 14), but
- linear OA(2152, 179, F2, 72) (dual of [179, 27, 73]-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 (81, 154, 193)-net over F2 | [i] | m-Reduction | |