Information on Result #599771
There is no digital (2, 12, 36)-net over F7, because extracting embedded orthogonal array would yield linear OA(712, 36, F7, 10) (dual of [36, 24, 11]-code), but
- construction Y1 [i] would yield
- linear OA(711, 15, F7, 10) (dual of [15, 4, 11]-code), but
- “BPM†bound on codes from Brouwer’s database [i]
- linear OA(724, 36, F7, 21) (dual of [36, 12, 22]-code), but
- discarding factors / shortening the dual code would yield linear OA(724, 31, F7, 21) (dual of [31, 7, 22]-code), but
- residual code [i] would yield OA(73, 9, S7, 3), but
- discarding factors / shortening the dual code would yield linear OA(724, 31, F7, 21) (dual of [31, 7, 22]-code), but
- linear OA(711, 15, F7, 10) (dual of [15, 4, 11]-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, 13, 36)-net over F7 | [i] | m-Reduction | |