Information on Result #598735
There is no digital (83, 157, 210)-net over F2, because extracting embedded orthogonal array would yield linear OA(2157, 210, F2, 74) (dual of [210, 53, 75]-code), but
- construction Y1 [i] would yield
- linear OA(2156, 190, F2, 74) (dual of [190, 34, 75]-code), but
- construction Y1 [i] would yield
- linear OA(2155, 178, F2, 74) (dual of [178, 23, 75]-code), but
- adding a parity check bit [i] would yield linear OA(2156, 179, F2, 75) (dual of [179, 23, 76]-code), but
- OA(234, 190, 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(2155, 178, F2, 74) (dual of [178, 23, 75]-code), but
- construction Y1 [i] would yield
- OA(253, 210, S2, 20), but
- discarding factors would yield OA(253, 182, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 9064 436853 738748 > 253 [i]
- discarding factors would yield OA(253, 182, S2, 20), but
- linear OA(2156, 190, F2, 74) (dual of [190, 34, 75]-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 (83, 158, 210)-net over F2 | [i] | m-Reduction | |