Information on Result #599574
There is no digital (59, 227, 272)-net over F4, because extracting embedded orthogonal array would yield linear OA(4227, 272, F4, 168) (dual of [272, 45, 169]-code), but
- residual code [i] would yield OA(459, 103, S4, 42), but
- the linear programming bound shows that M ≥ 20 209278 630007 954817 311657 592716 406577 471235 077989 401051 636395 089582 131646 221319 183990 947510 747136 / 59 997456 042944 145499 206694 218235 767252 553003 337898 939171 700875 > 459 [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 (59, 228, 272)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (59, 229, 272)-net over F4 | [i] | ||
| 3 | No digital (59, 230, 272)-net over F4 | [i] | ||