Information on Result #599756
There is no digital (31, 136, 252)-net over F5, because extracting embedded orthogonal array would yield linear OA(5136, 252, F5, 105) (dual of [252, 116, 106]-code), but
- residual code [i] would yield OA(531, 146, S5, 21), but
- 1 times truncation [i] would yield OA(530, 145, S5, 20), but
- the linear programming bound shows that M ≥ 34078 027381 828650 342719 814777 374267 578125 / 36 570326 005604 057357 > 530 [i]
- 1 times truncation [i] would yield OA(530, 145, S5, 20), 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 (31, 137, 252)-net over F5 | [i] | m-Reduction | |
| 2 | No digital (31, 138, 252)-net over F5 | [i] | ||
| 3 | No digital (31, 139, 252)-net over F5 | [i] | ||