Information on Result #3148078
There is no digital (40, 163, 172)-net over F4, because 3 times m-reduction would yield digital (40, 160, 172)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(4160, 172, F4, 120) (dual of [172, 12, 121]-code), but
- construction Y1 [i] would yield
- linear OA(4159, 166, F4, 120) (dual of [166, 7, 121]-code), but
- residual code [i] would yield linear OA(439, 45, F4, 30) (dual of [45, 6, 31]-code), but
- OA(412, 172, S4, 6), but
- discarding factors would yield OA(412, 156, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 16 866019 > 412 [i]
- discarding factors would yield OA(412, 156, S4, 6), but
- linear OA(4159, 166, F4, 120) (dual of [166, 7, 121]-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.