Information on Result #598660
There is no digital (69, 131, 165)-net over F2, because extracting embedded orthogonal array would yield linear OA(2131, 165, F2, 62) (dual of [165, 34, 63]-code), but
- construction Y1 [i] would yield
- linear OA(2130, 153, F2, 62) (dual of [153, 23, 63]-code), but
- adding a parity check bit [i] would yield linear OA(2131, 154, F2, 63) (dual of [154, 23, 64]-code), but
- OA(234, 165, S2, 12), but
- discarding factors would yield OA(234, 154, S2, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 17486 314616 > 234 [i]
- discarding factors would yield OA(234, 154, S2, 12), but
- linear OA(2130, 153, F2, 62) (dual of [153, 23, 63]-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 (69, 132, 165)-net over F2 | [i] | m-Reduction | |