Information on Result #3151562
There is no digital (5, 42, 53)-net over F8, because 1 times m-reduction would yield digital (5, 41, 53)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(841, 53, F8, 36) (dual of [53, 12, 37]-code), but
- construction Y1 [i] would yield
- linear OA(840, 43, F8, 36) (dual of [43, 3, 37]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(812, 53, F8, 10) (dual of [53, 41, 11]-code), but
- discarding factors / shortening the dual code would yield linear OA(812, 48, F8, 10) (dual of [48, 36, 11]-code), but
- construction Y1 [i] would yield
- linear OA(811, 16, F8, 10) (dual of [16, 5, 11]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- linear OA(836, 48, F8, 32) (dual of [48, 12, 33]-code), but
- discarding factors / shortening the dual code would yield linear OA(836, 43, F8, 32) (dual of [43, 7, 33]-code), but
- residual code [i] would yield OA(84, 10, S8, 4), but
- discarding factors / shortening the dual code would yield linear OA(836, 43, F8, 32) (dual of [43, 7, 33]-code), but
- linear OA(811, 16, F8, 10) (dual of [16, 5, 11]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(812, 48, F8, 10) (dual of [48, 36, 11]-code), but
- linear OA(840, 43, F8, 36) (dual of [43, 3, 37]-code), but
- construction Y1 [i] would yield
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
None.