Information on Result #599920
There is no digital (2, 50, 102)-net over F25, because extracting embedded orthogonal array would yield linear OA(2550, 102, F25, 48) (dual of [102, 52, 49]-code), but
- construction Y1 [i] would yield
- linear OA(2549, 52, F25, 48) (dual of [52, 3, 49]-code), but
- linear OA(2552, 102, F25, 50) (dual of [102, 50, 51]-code), but
- discarding factors / shortening the dual code would yield linear OA(2552, 78, F25, 50) (dual of [78, 26, 51]-code), but
- residual code [i] would yield OA(252, 27, S25, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 649 > 252 [i]
- residual code [i] would yield OA(252, 27, S25, 2), but
- discarding factors / shortening the dual code would yield linear OA(2552, 78, F25, 50) (dual of [78, 26, 51]-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 (2, 51, 102)-net over F25 | [i] | m-Reduction | |