Information on Result #3146921
There is no digital (5, 20, 40)-net over F4, because 1 times m-reduction would yield digital (5, 19, 40)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(419, 40, F4, 14) (dual of [40, 21, 15]-code), but
- construction Y1 [i] would yield
- linear OA(418, 24, F4, 14) (dual of [24, 6, 15]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- linear OA(421, 40, F4, 16) (dual of [40, 19, 17]-code), but
- discarding factors / shortening the dual code would yield linear OA(421, 32, F4, 16) (dual of [32, 11, 17]-code), but
- residual code [i] would yield OA(45, 15, S4, 4), but
- the linear programming bound shows that M ≥ 3328 / 3 > 45 [i]
- residual code [i] would yield OA(45, 15, S4, 4), but
- discarding factors / shortening the dual code would yield linear OA(421, 32, F4, 16) (dual of [32, 11, 17]-code), but
- linear OA(418, 24, F4, 14) (dual of [24, 6, 15]-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.