Information on Result #598903
There is no digital (132, 258, 291)-net over F2, because extracting embedded orthogonal array would yield linear OA(2258, 291, F2, 126) (dual of [291, 33, 127]-code), but
- construction Y1 [i] would yield
- linear OA(2257, 281, F2, 126) (dual of [281, 24, 127]-code), but
- residual code [i] would yield linear OA(2131, 154, F2, 63) (dual of [154, 23, 64]-code), but
- OA(233, 291, S2, 10), but
- discarding factors would yield OA(233, 254, S2, 10), but
- the Rao or (dual) Hamming bound shows that M ≥ 8640 218941 > 233 [i]
- discarding factors would yield OA(233, 254, S2, 10), but
- linear OA(2257, 281, F2, 126) (dual of [281, 24, 127]-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 (132, 259, 291)-net over F2 | [i] | m-Reduction | |