Information on Result #598723
There is no digital (81, 151, 222)-net over F2, because extracting embedded orthogonal array would yield linear OA(2151, 222, F2, 70) (dual of [222, 71, 71]-code), but
- construction Y1 [i] would yield
- linear OA(2150, 194, F2, 70) (dual of [194, 44, 71]-code), but
- construction Y1 [i] would yield
- linear OA(2149, 178, F2, 70) (dual of [178, 29, 71]-code), but
- adding a parity check bit [i] would yield linear OA(2150, 179, F2, 71) (dual of [179, 29, 72]-code), but
- OA(244, 194, S2, 16), but
- discarding factors would yield OA(244, 173, S2, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 17 734855 699135 > 244 [i]
- discarding factors would yield OA(244, 173, S2, 16), but
- linear OA(2149, 178, F2, 70) (dual of [178, 29, 71]-code), but
- construction Y1 [i] would yield
- OA(271, 222, S2, 28), but
- discarding factors would yield OA(271, 209, S2, 28), but
- the Rao or (dual) Hamming bound shows that M ≥ 2400 648072 841355 873622 > 271 [i]
- discarding factors would yield OA(271, 209, S2, 28), but
- linear OA(2150, 194, F2, 70) (dual of [194, 44, 71]-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, 152, 222)-net over F2 | [i] | m-Reduction | |