Information on Result #599464
There is no digital (45, 165, 251)-net over F4, because extracting embedded orthogonal array would yield linear OA(4165, 251, F4, 120) (dual of [251, 86, 121]-code), but
- residual code [i] would yield OA(445, 130, S4, 30), but
- the linear programming bound shows that M ≥ 18361 010361 194259 039988 478818 345052 021927 082904 773350 916096 / 14 690690 202506 322671 084018 635999 > 445 [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 (45, 166, 251)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (45, 167, 251)-net over F4 | [i] | ||
| 3 | No digital (45, 168, 251)-net over F4 | [i] | ||