Information on Result #3152353
There is no digital (3, 29, 58)-net over F9, because 1 times m-reduction would yield digital (3, 28, 58)-net over F9, but
- extracting embedded orthogonal array [i] would yield linear OA(928, 58, F9, 25) (dual of [58, 30, 26]-code), but
- construction Y1 [i] would yield
- OA(927, 31, S9, 25), but
- the linear programming bound shows that M ≥ 25644 034018 340666 323462 064529 / 377 > 927 [i]
- linear OA(930, 58, F9, 27) (dual of [58, 28, 28]-code), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), but
- residual code [i] would yield OA(93, 11, S9, 3), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), but
- OA(927, 31, S9, 25), 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.