Information on Result #3151423
There is no digital (4, 38, 41)-net over F8, because 2 times m-reduction would yield digital (4, 36, 41)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(836, 41, F8, 32) (dual of [41, 5, 33]-code), but
- construction Y1 [i] would yield
- OA(835, 37, S8, 32), but
- the (dual) Plotkin bound shows that M ≥ 1622 592768 292133 633915 780102 881280 / 33 > 835 [i]
- OA(85, 41, S8, 4), but
- discarding factors would yield OA(85, 37, S8, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 32894 > 85 [i]
- discarding factors would yield OA(85, 37, S8, 4), but
- OA(835, 37, S8, 32), 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.