Information on Result #599801
There is no digital (2, 10, 55)-net over F8, because extracting embedded orthogonal array would yield linear OA(810, 55, F8, 8) (dual of [55, 45, 9]-code), but
- construction Y1 [i] would yield
- linear OA(89, 15, F8, 8) (dual of [15, 6, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- OA(845, 55, S8, 40), but
- discarding factors would yield OA(845, 52, S8, 40), but
- the linear programming bound shows that M ≥ 17082 370822 074457 326416 360196 848644 913580 998656 / 353625 > 845 [i]
- discarding factors would yield OA(845, 52, S8, 40), but
- linear OA(89, 15, F8, 8) (dual of [15, 6, 9]-code), but
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 (2, 11, 55)-net over F8 | [i] | m-Reduction | |