Information on Result #598651
There is no digital (66, 124, 166)-net over F2, because extracting embedded orthogonal array would yield linear OA(2124, 166, F2, 58) (dual of [166, 42, 59]-code), but
- construction Y1 [i] would yield
- OA(2123, 150, S2, 58), but
- the linear programming bound shows that M ≥ 36000 467012 365704 432940 148948 904738 978722 217984 / 3201 323125 > 2123 [i]
- OA(242, 166, S2, 16), but
- discarding factors would yield OA(242, 146, S2, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 4 467697 956730 > 242 [i]
- discarding factors would yield OA(242, 146, S2, 16), but
- OA(2123, 150, S2, 58), 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 (66, 125, 166)-net over F2 | [i] | m-Reduction | |