Information on Result #3151381
There is no digital (3, 138, 34)-net over F8, because 111 times m-reduction would yield digital (3, 27, 34)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(827, 34, F8, 24) (dual of [34, 7, 25]-code), but
- construction Y1 [i] would yield
- OA(826, 28, S8, 24), but
- the (dual) Plotkin bound shows that M ≥ 9 671406 556917 033397 649408 / 25 > 826 [i]
- OA(87, 34, S8, 6), but
- discarding factors would yield OA(87, 32, S8, 6), but
- the linear programming bound shows that M ≥ 3784 900608 / 1729 > 87 [i]
- discarding factors would yield OA(87, 32, S8, 6), but
- OA(826, 28, S8, 24), 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.