Information on Result #598790
There is no digital (92, 174, 228)-net over F2, because extracting embedded orthogonal array would yield linear OA(2174, 228, F2, 82) (dual of [228, 54, 83]-code), but
- construction Y1 [i] would yield
- linear OA(2173, 208, F2, 82) (dual of [208, 35, 83]-code), but
- construction Y1 [i] would yield
- linear OA(2172, 196, F2, 82) (dual of [196, 24, 83]-code), but
- adding a parity check bit [i] would yield linear OA(2173, 197, F2, 83) (dual of [197, 24, 84]-code), but
- OA(235, 208, S2, 12), but
- discarding factors would yield OA(235, 173, S2, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 35365 229344 > 235 [i]
- discarding factors would yield OA(235, 173, S2, 12), but
- linear OA(2172, 196, F2, 82) (dual of [196, 24, 83]-code), but
- construction Y1 [i] would yield
- OA(254, 228, S2, 20), but
- discarding factors would yield OA(254, 195, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 18304 094847 646336 > 254 [i]
- discarding factors would yield OA(254, 195, S2, 20), but
- linear OA(2173, 208, F2, 82) (dual of [208, 35, 83]-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 (92, 175, 228)-net over F2 | [i] | m-Reduction | |