Information on Result #598645
There is no digital (63, 117, 168)-net over F2, because extracting embedded orthogonal array would yield linear OA(2117, 168, F2, 54) (dual of [168, 51, 55]-code), but
- construction Y1 [i] would yield
- OA(2116, 148, S2, 54), but
- the linear programming bound shows that M ≥ 67 089316 460630 621624 223128 238837 181334 945792 / 674 571975 > 2116 [i]
- OA(251, 168, S2, 20), but
- discarding factors would yield OA(251, 159, S2, 20), but
- the Rao or (dual) Hamming bound shows that M ≥ 2282 987168 569557 > 251 [i]
- discarding factors would yield OA(251, 159, S2, 20), but
- OA(2116, 148, S2, 54), 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 (63, 118, 168)-net over F2 | [i] | m-Reduction | |