Information on Result #598661
There is no digital (69, 133, 160)-net over F2, because extracting embedded orthogonal array would yield linear OA(2133, 160, F2, 64) (dual of [160, 27, 65]-code), but
- construction Y1 [i] would yield
- OA(2132, 150, S2, 64), but
- the linear programming bound shows that M ≥ 7654 730789 395636 393332 135297 086550 086927 777792 / 1 285141 > 2132 [i]
- OA(227, 160, S2, 10), but
- discarding factors would yield OA(227, 111, S2, 10), but
- the Rao or (dual) Hamming bound shows that M ≥ 134 381744 > 227 [i]
- discarding factors would yield OA(227, 111, S2, 10), but
- OA(2132, 150, S2, 64), 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 (69, 134, 160)-net over F2 | [i] | m-Reduction | |