Information on Result #599540
There is no digital (56, 196, 345)-net over F4, because extracting embedded orthogonal array would yield linear OA(4196, 345, F4, 140) (dual of [345, 149, 141]-code), but
- residual code [i] would yield OA(456, 204, S4, 35), but
- the linear programming bound shows that M ≥ 78295 866271 954113 495370 355913 581218 786159 455204 222712 111589 032673 922357 657600 / 14 695871 573792 476851 963908 736113 155530 258961 > 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, 197, 345)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (56, 198, 345)-net over F4 | [i] | ||
| 3 | No digital (56, 199, 345)-net over F4 | [i] | ||