Information on Result #1186694
Digital (154, 171, 1048624)-net over F4, using net defined by OOA based on linear OOA(4171, 1048624, F4, 18, 17) (dual of [(1048624, 18), 18875061, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4171, 4194497, F4, 2, 17) (dual of [(4194497, 2), 8388823, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4169, 4194496, F4, 2, 17) (dual of [(4194496, 2), 8388823, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(424, 195, F4, 2, 8) (dual of [(195, 2), 366, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 24, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 8, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 8, 65)-net over F64, using
- extracting embedded OOA [i] based on digital (16, 24, 195)-net over F4, using
- linear OOA(4145, 4194301, F4, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- linear OOA(424, 195, F4, 2, 8) (dual of [(195, 2), 366, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4169, 4194496, F4, 2, 17) (dual of [(4194496, 2), 8388823, 18]-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.