Information on Result #599539
There is no digital (56, 192, 374)-net over F4, because extracting embedded orthogonal array would yield linear OA(4192, 374, F4, 136) (dual of [374, 182, 137]-code), but
- residual code [i] would yield OA(456, 237, S4, 34), but
- the linear programming bound shows that M ≥ 227 819482 170490 726334 286831 192651 607943 130369 749048 513507 843112 960000 000000 / 43777 691396 586787 052635 611770 906797 710989 > 456 [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 (56, 193, 374)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (56, 194, 374)-net over F4 | [i] | ||
| 3 | No digital (56, 195, 374)-net over F4 | [i] | ||