Information on Result #599552
There is no digital (57, 209, 307)-net over F4, because extracting embedded orthogonal array would yield linear OA(4209, 307, F4, 152) (dual of [307, 98, 153]-code), but
- residual code [i] would yield OA(457, 154, S4, 38), but
- the linear programming bound shows that M ≥ 797207 451366 565965 705395 219386 483301 387169 888973 699524 917197 426960 177348 462205 201075 404800 / 37 245253 436418 517434 670471 565022 824982 371808 117558 951421 > 457 [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 (57, 210, 307)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (57, 211, 307)-net over F4 | [i] | ||
| 3 | No digital (57, 212, 307)-net over F4 | [i] | ||