Information on Result #599512
There is no digital (52, 192, 279)-net over F4, because extracting embedded orthogonal array would yield linear OA(4192, 279, F4, 140) (dual of [279, 87, 141]-code), but
- residual code [i] would yield OA(452, 138, S4, 35), but
- the linear programming bound shows that M ≥ 14 564003 487067 138043 331719 274369 344824 206731 992337 689402 817088 211676 748054 528000 / 703008 083798 117523 214095 285089 936359 793876 700683 > 452 [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 (52, 193, 279)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (52, 194, 279)-net over F4 | [i] | ||
| 3 | No digital (52, 195, 279)-net over F4 | [i] | ||