Information on Result #599465
There is no digital (45, 169, 237)-net over F4, because extracting embedded orthogonal array would yield linear OA(4169, 237, F4, 124) (dual of [237, 68, 125]-code), but
- residual code [i] would yield OA(445, 112, S4, 31), but
- the linear programming bound shows that M ≥ 30 703316 954186 650166 302103 088413 940385 262854 668690 715040 548493 721600 / 24108 147423 127287 645158 347013 987588 540153 > 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, 170, 237)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (45, 171, 237)-net over F4 | [i] | ||
| 3 | No digital (45, 172, 237)-net over F4 | [i] | ||