Information on Result #598816
There is no digital (98, 184, 249)-net over F2, because extracting embedded orthogonal array would yield linear OA(2184, 249, F2, 86) (dual of [249, 65, 87]-code), but
- construction Y1 [i] would yield
- linear OA(2183, 225, F2, 86) (dual of [225, 42, 87]-code), but
- construction Y1 [i] would yield
- linear OA(2182, 211, F2, 86) (dual of [211, 29, 87]-code), but
- adding a parity check bit [i] would yield linear OA(2183, 212, F2, 87) (dual of [212, 29, 88]-code), but
- OA(242, 225, S2, 14), but
- discarding factors would yield OA(242, 219, S2, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 498367 189624 > 242 [i]
- discarding factors would yield OA(242, 219, S2, 14), but
- linear OA(2182, 211, F2, 86) (dual of [211, 29, 87]-code), but
- construction Y1 [i] would yield
- OA(265, 249, S2, 24), but
- discarding factors would yield OA(265, 231, S2, 24), but
- the Rao or (dual) Hamming bound shows that M ≥ 38 110539 835438 477924 > 265 [i]
- discarding factors would yield OA(265, 231, S2, 24), but
- linear OA(2183, 225, F2, 86) (dual of [225, 42, 87]-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 (98, 185, 249)-net over F2 | [i] | m-Reduction | |