Information on Result #598899
There is no digital (131, 255, 288)-net over F2, because extracting embedded orthogonal array would yield linear OA(2255, 288, F2, 124) (dual of [288, 33, 125]-code), but
- construction Y1 [i] would yield
- linear OA(2254, 278, F2, 124) (dual of [278, 24, 125]-code), but
- residual code [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
- residual code [i] would yield linear OA(2130, 153, F2, 62) (dual of [153, 23, 63]-code), but
- OA(233, 288, 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(2254, 278, F2, 124) (dual of [278, 24, 125]-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 (131, 256, 288)-net over F2 | [i] | m-Reduction | |