Information on Result #599532
There is no digital (55, 199, 309)-net over F4, because extracting embedded orthogonal array would yield linear OA(4199, 309, F4, 144) (dual of [309, 110, 145]-code), but
- residual code [i] would yield OA(455, 164, S4, 36), but
- the linear programming bound shows that M ≥ 980 201801 606598 702017 212850 515741 792418 086779 414793 869747 648944 529897 580134 400000 / 752717 700220 343776 849584 966340 992475 812762 611911 > 455 [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 (55, 200, 309)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (55, 201, 309)-net over F4 | [i] | ||
| 3 | No digital (55, 202, 309)-net over F4 | [i] | ||