MinT - Information on Result #1224943

Information on Result #1224943

Digital (39, 54, 4758)-net over F₃₂, using (u,Â u+v)-construction based on

digital (4, 11, 77)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 33)-net over F₃₂, using
    - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
        the rational function field F₃₂(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 8, 44)-net over F₃₂, using
    - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
digital (28, 43, 4681)-net over F₃₂, using
- net defined by OOA [i] based on linear OOA(32⁴³, 4681, F₃₂, 15, 15) (dual of [(4681, 15), 70172, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(32⁴³, 32768, F₃₂, 15) (dual of [32768, 32725, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

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