Information on Result #599480
There is no digital (47, 175, 250)-net over F4, because extracting embedded orthogonal array would yield linear OA(4175, 250, F4, 128) (dual of [250, 75, 129]-code), but
- residual code [i] would yield OA(447, 121, S4, 32), but
- the linear programming bound shows that M ≥ 365 129709 190376 390301 373618 637040 010384 793045 585047 102752 276086 784000 / 18163 087858 506659 594163 938688 475283 050507 > 447 [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 (47, 176, 250)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (47, 177, 250)-net over F4 | [i] | ||
| 3 | No digital (47, 178, 250)-net over F4 | [i] | ||