Information on Result #599445
There is no digital (42, 158, 223)-net over F4, because extracting embedded orthogonal array would yield linear OA(4158, 223, F4, 116) (dual of [223, 65, 117]-code), but
- residual code [i] would yield OA(442, 106, S4, 29), but
- the linear programming bound shows that M ≥ 11 515430 185021 615009 307015 123093 343331 130678 608727 482845 042118 230016 / 573326 282922 594402 886717 422034 435890 047071 > 442 [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 (42, 159, 223)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (42, 160, 223)-net over F4 | [i] | ||
| 3 | No digital (42, 161, 223)-net over F4 | [i] | ||