Information on Result #598783
There is no digital (91, 171, 235)-net over F2, because extracting embedded orthogonal array would yield linear OA(2171, 235, F2, 80) (dual of [235, 64, 81]-code), but
- construction Y1 [i] would yield
- linear OA(2170, 211, F2, 80) (dual of [211, 41, 81]-code), but
- construction Y1 [i] would yield
- linear OA(2169, 197, F2, 80) (dual of [197, 28, 81]-code), but
- adding a parity check bit [i] would yield linear OA(2170, 198, F2, 81) (dual of [198, 28, 82]-code), but
- OA(241, 211, S2, 14), but
- discarding factors would yield OA(241, 198, S2, 14), but
- the Rao or (dual) Hamming bound shows that M ≥ 2 206433 399776 > 241 [i]
- discarding factors would yield OA(241, 198, S2, 14), but
- linear OA(2169, 197, F2, 80) (dual of [197, 28, 81]-code), but
- construction Y1 [i] would yield
- OA(264, 235, S2, 24), but
- discarding factors would yield OA(264, 218, S2, 24), but
- the Rao or (dual) Hamming bound shows that M ≥ 18 753208 478511 637348 > 264 [i]
- discarding factors would yield OA(264, 218, S2, 24), but
- linear OA(2170, 211, F2, 80) (dual of [211, 41, 81]-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 (91, 172, 235)-net over F2 | [i] | m-Reduction | |