Information on Result #3149369
There is no digital (55, 218, 238)-net over F4, because 3 times m-reduction would yield digital (55, 215, 238)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(4215, 238, F4, 160) (dual of [238, 23, 161]-code), but
- construction Y1 [i] would yield
- linear OA(4214, 226, F4, 160) (dual of [226, 12, 161]-code), but
- construction Y1 [i] would yield
- linear OA(4213, 220, F4, 160) (dual of [220, 7, 161]-code), but
- residual code [i] would yield linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-code), but
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- residual code [i] would yield linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-code), but
- OA(412, 226, S4, 6), but
- discarding factors would yield OA(412, 156, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 16 866019 > 412 [i]
- discarding factors would yield OA(412, 156, S4, 6), but
- linear OA(4213, 220, F4, 160) (dual of [220, 7, 161]-code), but
- construction Y1 [i] would yield
- OA(423, 238, S4, 12), but
- discarding factors would yield OA(423, 205, S4, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 70 503355 038244 > 423 [i]
- discarding factors would yield OA(423, 205, S4, 12), but
- linear OA(4214, 226, F4, 160) (dual of [226, 12, 161]-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.