Information on Result #1215419
Digital (133, 148, 2407675)-net over F8, using (u, u+v)-construction based on
- digital (27, 34, 10933)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (24, 31, 10924)-net over F8, using
- net defined by OOA [i] based on linear OOA(831, 10924, F8, 7, 7) (dual of [(10924, 7), 76437, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(831, 32773, F8, 7) (dual of [32773, 32742, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(831, 32768, F8, 7) (dual of [32768, 32737, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(826, 32768, F8, 6) (dual of [32768, 32742, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(831, 32773, F8, 7) (dual of [32773, 32742, 8]-code), using
- net defined by OOA [i] based on linear OOA(831, 10924, F8, 7, 7) (dual of [(10924, 7), 76437, 8]-NRT-code), using
- digital (0, 3, 9)-net over F8, using
- (u, u+v)-construction [i] based on
- 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.