Information on Result #599761
There is no digital (32, 142, 248)-net over F5, because extracting embedded orthogonal array would yield linear OA(5142, 248, F5, 110) (dual of [248, 106, 111]-code), but
- residual code [i] would yield OA(532, 137, S5, 22), but
- the linear programming bound shows that M ≥ 49811 417030 749528 748174 208068 847656 250000 / 2 010328 776131 927263 > 532 [i]
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 (32, 143, 248)-net over F5 | [i] | m-Reduction | |
| 2 | No digital (32, 144, 248)-net over F5 | [i] | ||
| 3 | No digital (32, 145, 248)-net over F5 | [i] | ||
| 4 | No digital (32, 146, 248)-net over F5 | [i] | ||