Information on Result #3151262
There is no digital (2, 17, 32)-net over F8, because 3 times m-reduction would yield digital (2, 14, 32)-net over F8, but
- extracting embedded orthogonal array [i] would yield linear OA(814, 32, F8, 12) (dual of [32, 18, 13]-code), but
- construction Y1 [i] would yield
- linear OA(813, 16, F8, 12) (dual of [16, 3, 13]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- linear OA(818, 32, F8, 16) (dual of [32, 14, 17]-code), but
- discarding factors / shortening the dual code would yield linear OA(818, 27, F8, 16) (dual of [27, 9, 17]-code), but
- residual code [i] would yield OA(82, 10, S8, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 71 > 82 [i]
- residual code [i] would yield OA(82, 10, S8, 2), but
- discarding factors / shortening the dual code would yield linear OA(818, 27, F8, 16) (dual of [27, 9, 17]-code), but
- linear OA(813, 16, F8, 12) (dual of [16, 3, 13]-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.