Information on Result #3151987
There is no digital (20, 163, 173)-net over F8, because 7 times m-reduction would yield digital (20, 156, 173)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(8156, 173, F8, 136) (dual of [173, 17, 137]-code), but
- construction Y1 [i] would yield
- linear OA(8155, 161, F8, 136) (dual of [161, 6, 137]-code), but
- construction Y1 [i] would yield
- linear OA(8154, 157, F8, 136) (dual of [157, 3, 137]-code), but
- OA(86, 161, S8, 4), but
- discarding factors would yield OA(86, 104, S8, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 263173 > 86 [i]
- discarding factors would yield OA(86, 104, S8, 4), but
- construction Y1 [i] would yield
- OA(817, 173, S8, 12), but
- discarding factors would yield OA(817, 158, S8, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 2322 300560 650316 > 817 [i]
- discarding factors would yield OA(817, 158, S8, 12), but
- linear OA(8155, 161, F8, 136) (dual of [161, 6, 137]-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.