MinT - Information on Result #1227787

Information on Result #1227787

Digital (58, 74, 1048757)-net over F₈₁, using (u,Â u+v)-construction based on

digital (5, 13, 182)-net over F₈₁, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 4, 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, 9, 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 (45, 61, 1048575)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁶¹, 1048575, F₈₁, 16, 16) (dual of [(1048575, 16), 16777139, 17]-NRT-code), using
  - OA 8-folding and stacking [i] based on linear OA(81⁶¹, 8388600, F₈₁, 16) (dual of [8388600, 8388539, 17]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁶¹, large, F₈₁, 16) (dual of [large, large−61, 17]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

None.

None.