Information on Result #3146303
There is no digital (68, 205, 216)-net over F3, because 2 times m-reduction would yield digital (68, 203, 216)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3203, 216, F3, 135) (dual of [216, 13, 136]-code), but
- construction Y1 [i] would yield
- linear OA(3202, 210, F3, 135) (dual of [210, 8, 136]-code), but
- residual code [i] would yield linear OA(367, 74, F3, 45) (dual of [74, 7, 46]-code), but
- residual code [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- “HHM†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- residual code [i] would yield linear OA(367, 74, F3, 45) (dual of [74, 7, 46]-code), but
- OA(313, 216, S3, 6), but
- discarding factors would yield OA(313, 107, S3, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 1 610779 > 313 [i]
- discarding factors would yield OA(313, 107, S3, 6), but
- linear OA(3202, 210, F3, 135) (dual of [210, 8, 136]-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.