Information on Result #3148299
There is no digital (42, 167, 188)-net over F4, because 1 times m-reduction would yield digital (42, 166, 188)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(4166, 188, F4, 124) (dual of [188, 22, 125]-code), but
- construction Y1 [i] would yield
- linear OA(4165, 176, F4, 124) (dual of [176, 11, 125]-code), but
- residual code [i] would yield linear OA(441, 51, F4, 31) (dual of [51, 10, 32]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(441, 51, F4, 31) (dual of [51, 10, 32]-code), but
- OA(422, 188, S4, 12), but
- discarding factors would yield OA(422, 164, S4, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 18 187369 733464 > 422 [i]
- discarding factors would yield OA(422, 164, S4, 12), but
- linear OA(4165, 176, F4, 124) (dual of [176, 11, 125]-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.