Information on Result #1192156
Digital (146, 164, 1864220)-net over F8, using net defined by OOA based on linear OOA(8164, 1864220, F8, 21, 18) (dual of [(1864220, 21), 39148456, 19]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8164, 5592661, F8, 3, 18) (dual of [(5592661, 3), 16777819, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8164, 5592662, F8, 3, 18) (dual of [(5592662, 3), 16777822, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(826, 260, F8, 3, 9) (dual of [(260, 3), 754, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(88, 130, F8, 3, 4) (dual of [(130, 3), 382, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 8, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 4, 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, 4, 65)-net over F64, using
- extracting embedded OOA [i] based on digital (4, 8, 130)-net over F8, using
- linear OOA(818, 130, F8, 3, 9) (dual of [(130, 3), 372, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (9, 18, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 9, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- trace code for nets [i] based on digital (0, 9, 65)-net over F64, using
- extracting embedded OOA [i] based on digital (9, 18, 130)-net over F8, using
- linear OOA(88, 130, F8, 3, 4) (dual of [(130, 3), 382, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8138, 5592402, F8, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
- trace code [i] based on linear OOA(6469, 2796201, F64, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 3-folding [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- trace code [i] based on linear OOA(6469, 2796201, F64, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
- linear OOA(826, 260, F8, 3, 9) (dual of [(260, 3), 754, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8164, 5592662, F8, 3, 18) (dual of [(5592662, 3), 16777822, 19]-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.