Information on Result #599453
There is no digital (43, 167, 209)-net over F4, because extracting embedded orthogonal array would yield linear OA(4167, 209, F4, 124) (dual of [209, 42, 125]-code), but
- residual code [i] would yield OA(443, 84, S4, 31), but
- the linear programming bound shows that M ≥ 743 432824 923585 138466 079893 608385 692163 936496 473876 252564 706270 846821 427655 153621 009913 103585 162421 132960 451704 728431 099904 / 9 052373 288486 345160 206941 767894 606217 335850 613093 145925 916389 354432 331859 732314 014078 839167 611385 > 443 [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 (43, 168, 209)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (43, 169, 209)-net over F4 | [i] | ||
| 3 | No digital (43, 170, 209)-net over F4 | [i] | ||