Information on Result #599658
There is no digital (68, 232, 443)-net over F4, because extracting embedded orthogonal array would yield linear OA(4232, 443, F4, 164) (dual of [443, 211, 165]-code), but
- residual code [i] would yield OA(468, 278, S4, 41), but
- the linear programming bound shows that M ≥ 9751 854148 120896 570793 936092 472808 488071 901083 469159 873923 045115 979366 400000 000000 000000 / 106042 296287 604630 552636 245594 756356 027986 690833 > 468 [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 (68, 233, 443)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (68, 234, 443)-net over F4 | [i] | ||
| 3 | No digital (68, 235, 443)-net over F4 | [i] | ||