Information on Result #1192038
Digital (112, 129, 1048607)-net over F8, using net defined by OOA based on linear OOA(8129, 1048607, F8, 18, 17) (dual of [(1048607, 18), 18874797, 18]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8129, 4194429, F8, 2, 17) (dual of [(4194429, 2), 8388729, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8129, 4194431, F8, 2, 17) (dual of [(4194431, 2), 8388733, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(816, 130, F8, 2, 8) (dual of [(130, 2), 244, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 16, 130)-net over F8, 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 (8, 16, 130)-net over F8, using
- linear OOA(8113, 4194301, F8, 2, 17) (dual of [(4194301, 2), 8388489, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8113, 8388602, F8, 17) (dual of [8388602, 8388489, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, large, F8, 17) (dual of [large, large−113, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, 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(8113, large, F8, 17) (dual of [large, large−113, 18]-code), using
- OOA 2-folding [i] based on linear OA(8113, 8388602, F8, 17) (dual of [8388602, 8388489, 18]-code), using
- linear OOA(816, 130, F8, 2, 8) (dual of [(130, 2), 244, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8129, 4194431, F8, 2, 17) (dual of [(4194431, 2), 8388733, 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.