MinT - Information on Result #1227888

Information on Result #1227888

Digital (54, 74, 53326)-net over F₈₁, using (u,Â u+v)-construction based on

digital (6, 16, 182)-net over F₈₁, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 5, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 11, 100)-net over F₈₁, using
    - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
        a function field by SÃ©mirat [i]
digital (38, 58, 53144)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁵⁸, 53144, F₈₁, 20, 20) (dual of [(53144, 20), 1062822, 21]-NRT-code), using
  - OA 10-folding and stacking [i] based on linear OA(81⁵⁸, 531440, F₈₁, 20) (dual of [531440, 531382, 21]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁵⁸, 531441, F₈₁, 20) (dual of [531441, 531383, 21]-code), using
      - an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]

Mode: Constructive and linear.

None.

None.