Information on Result #3144421
There is no digital (36, 161, 117)-net over F3, because 53 times m-reduction would yield digital (36, 108, 117)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3108, 117, F3, 72) (dual of [117, 9, 73]-code), but
- construction Y1 [i] would yield
- linear OA(3107, 113, F3, 72) (dual of [113, 6, 73]-code), but
- residual code [i] would yield linear OA(335, 40, F3, 24) (dual of [40, 5, 25]-code), but
- “vE1†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(335, 40, F3, 24) (dual of [40, 5, 25]-code), but
- OA(39, 117, S3, 4), but
- discarding factors would yield OA(39, 100, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 20001 > 39 [i]
- discarding factors would yield OA(39, 100, S3, 4), but
- linear OA(3107, 113, F3, 72) (dual of [113, 6, 73]-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.