Information on Result #1211306
Digital (153, 180, 5059)-net over F4, using (u, u+v)-construction based on
- digital (5, 18, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (135, 162, 5042)-net over F4, using
- net defined by OOA [i] based on linear OOA(4162, 5042, F4, 27, 27) (dual of [(5042, 27), 135972, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4162, 65547, F4, 27) (dual of [65547, 65385, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4162, 65554, F4, 27) (dual of [65554, 65392, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(4161, 65537, F4, 27) (dual of [65537, 65376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(41, 17, F4, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4162, 65554, F4, 27) (dual of [65554, 65392, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4162, 65547, F4, 27) (dual of [65547, 65385, 28]-code), using
- net defined by OOA [i] based on linear OOA(4162, 5042, F4, 27, 27) (dual of [(5042, 27), 135972, 28]-NRT-code), using
Mode: Constructive and 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.