Information on Result #3151646
There is no digital (5, 127, 50)-net over F8, because 82 times m-reduction would yield digital (5, 45, 50)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(845, 50, F8, 40) (dual of [50, 5, 41]-code), but
- construction Y1 [i] would yield
- OA(844, 46, S8, 40), but
- the (dual) Plotkin bound shows that M ≥ 261336 857795 280739 939871 698507 597986 398208 / 41 > 844 [i]
- OA(85, 50, 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(844, 46, S8, 40), 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.