Information on Result #598662
There is no digital (69, 135, 158)-net over F2, because extracting embedded orthogonal array would yield linear OA(2135, 158, F2, 66) (dual of [158, 23, 67]-code), but
- construction Y1 [i] would yield
- OA(2134, 150, S2, 66), but
- the linear programming bound shows that M ≥ 235 377396 587616 186439 177776 455843 253082 652672 / 10387 > 2134 [i]
- OA(223, 158, S2, 8), but
- discarding factors would yield OA(223, 120, S2, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 8 502671 > 223 [i]
- discarding factors would yield OA(223, 120, S2, 8), but
- OA(2134, 150, S2, 66), 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, 136, 158)-net over F2 | [i] | m-Reduction | |