Information on Result #1215408
Digital (122, 137, 2397147)-net over F8, using (u, u+v)-construction based on
- digital (16, 23, 405)-net over F8, using
- net defined by OOA [i] based on linear OOA(823, 405, F8, 9, 7) (dual of [(405, 9), 3622, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(823, 406, F8, 3, 7) (dual of [(406, 3), 1195, 8]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(81, 73, F8, 3, 1) (dual of [(73, 3), 218, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(81, s, F8, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(81, s, F8, 3, 1) for arbitrarily large s, using
- linear OOA(83, 73, F8, 3, 2) (dual of [(73, 3), 216, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- Hamming code H(3,8) [i]
- appending kth column [i] based on linear OA(83, 73, F8, 2) (dual of [73, 70, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(83, 73, F8, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- linear OOA(85, 130, F8, 3, 3) (dual of [(130, 3), 385, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(85, 207, F8, 3, 3) (dual of [(207, 3), 616, 4]-NRT-code), using
- linear OOA(814, 130, F8, 3, 7) (dual of [(130, 3), 376, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 7, 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, 7, 65)-net over F64, using
- extracting embedded OOA [i] based on digital (7, 14, 130)-net over F8, using
- linear OOA(81, 73, F8, 3, 1) (dual of [(73, 3), 218, 2]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(823, 406, F8, 3, 7) (dual of [(406, 3), 1195, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(823, 405, F8, 9, 7) (dual of [(405, 9), 3622, 8]-NRT-code), using
- digital (99, 114, 2396742)-net over F8, using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F64, using
- net defined by OOA [i] based on linear OOA(6457, 1198371, F64, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6457, 8388598, F64, 15) (dual of [8388598, 8388541, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6457, 8388598, F64, 15) (dual of [8388598, 8388541, 16]-code), using
- net defined by OOA [i] based on linear OOA(6457, 1198371, F64, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F64, 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.