Information on Result #1234622
Digital (58, 70, 2796329)-net over F128, using generalized (u, u+v)-construction based on
- digital (0, 4, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (15, 21, 1398100)-net over F128, using
- s-reduction based on digital (15, 21, 2796201)-net over F128, using
- net defined by OOA [i] based on linear OOA(12821, 2796201, F128, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(12821, 2796201, F128, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- s-reduction based on digital (15, 21, 2796201)-net over F128, using
- digital (33, 45, 1398100)-net over F128, using
- net defined by OOA [i] based on linear OOA(12845, 1398100, F128, 12, 12) (dual of [(1398100, 12), 16777155, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(12845, 8388600, F128, 12) (dual of [8388600, 8388555, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9256395 | 1284−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(12845, large, F128, 12) (dual of [large, large−45, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(12845, 8388600, F128, 12) (dual of [8388600, 8388555, 13]-code), using
- net defined by OOA [i] based on linear OOA(12845, 1398100, F128, 12, 12) (dual of [(1398100, 12), 16777155, 13]-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.