Information on Result #599335
There is no digital (2, 8, 18)-net over F4, because extracting embedded orthogonal array would yield linear OA(48, 18, F4, 6) (dual of [18, 10, 7]-code), but
- construction Y1 [i] would yield
- linear OA(47, 10, F4, 6) (dual of [10, 3, 7]-code), but
- linear OA(410, 18, F4, 8) (dual of [18, 8, 9]-code), but
- discarding factors / shortening the dual code would yield linear OA(410, 15, F4, 8) (dual of [15, 5, 9]-code), but
- residual code [i] would yield OA(42, 6, S4, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 19 > 42 [i]
- residual code [i] would yield OA(42, 6, S4, 2), but
- discarding factors / shortening the dual code would yield linear OA(410, 15, F4, 8) (dual of [15, 5, 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, 9, 18)-net over F4 | [i] | m-Reduction | |