MinT - Information on Result #1228450

Information on Result #1228450

Digital (44, 68, 1686)-net over F₁₂₈, using (u,Â u+v)-construction based on

digital (9, 21, 321)-net over F₁₂₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 6, 129)-net over F₁₂₈, using
    - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ 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]
  2. digital (3, 15, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]
digital (23, 47, 1365)-net over F₁₂₈, using
- net defined by OOA [i] based on linear OOA(128⁴⁷, 1365, F₁₂₈, 24, 24) (dual of [(1365, 24), 32713, 25]-NRT-code), using
  - OA 12-folding and stacking [i] based on linear OA(128⁴⁷, 16380, F₁₂₈, 24) (dual of [16380, 16333, 25]-code), using
    - discarding factors / shortening the dual code based on linear OA(128⁴⁷, 16384, F₁₂₈, 24) (dual of [16384, 16337, 25]-code), using
      - an extension C_e(23) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 128²âˆ’1, defining interval IÂ =Â [1,23], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 24 [i]

Mode: Constructive and linear.

None.

None.