Information on Result #3150866
There is no digital (5, 63, 45)-net over F7, because 28 times m-reduction would yield digital (5, 35, 45)-net over F7, but
- extracting embedded orthogonal array [i] would yield linear OA(735, 45, F7, 30) (dual of [45, 10, 31]-code), but
- construction Y1 [i] would yield
- linear OA(734, 37, F7, 30) (dual of [37, 3, 31]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(710, 45, F7, 8) (dual of [45, 35, 9]-code), but
- discarding factors / shortening the dual code would yield linear OA(710, 42, F7, 8) (dual of [42, 32, 9]-code), but
- construction Y1 [i] would yield
- linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- linear OA(732, 42, F7, 28) (dual of [42, 10, 29]-code), but
- discarding factors / shortening the dual code would yield linear OA(732, 38, F7, 28) (dual of [38, 6, 29]-code), but
- linear OA(79, 14, F7, 8) (dual of [14, 5, 9]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(710, 42, F7, 8) (dual of [42, 32, 9]-code), but
- linear OA(734, 37, F7, 30) (dual of [37, 3, 31]-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.