Information on Result #598838
There is no digital (104, 196, 252)-net over F2, because extracting embedded orthogonal array would yield linear OA(2196, 252, F2, 92) (dual of [252, 56, 93]-code), but
- construction Y1 [i] would yield
- linear OA(2195, 232, F2, 92) (dual of [232, 37, 93]-code), but
- construction Y1 [i] would yield
- linear OA(2194, 220, F2, 92) (dual of [220, 26, 93]-code), but
- adding a parity check bit [i] would yield linear OA(2195, 221, F2, 93) (dual of [221, 26, 94]-code), but
- OA(237, 232, S2, 12), but
- discarding factors would yield OA(237, 217, S2, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 139173 045698 > 237 [i]
- discarding factors would yield OA(237, 217, S2, 12), but
- linear OA(2194, 220, F2, 92) (dual of [220, 26, 93]-code), but
- construction Y1 [i] would yield
- OA(256, 252, S2, 20), but
- discarding factors would yield OA(256, 224, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 74952 904195 135741 > 256 [i]
- discarding factors would yield OA(256, 224, S2, 20), but
- linear OA(2195, 232, F2, 92) (dual of [232, 37, 93]-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 (104, 197, 252)-net over F2 | [i] | m-Reduction | |
| 2 | No digital (104, 198, 252)-net over F2 | [i] | ||
| 3 | No digital (104, 199, 252)-net over F2 | [i] | ||