MinT - Information on Result #1234427

Information on Result #1234427

Digital (70, 89, 932261)-net over F₆₄, using (u,Â u+v)-construction based on

digital (7, 16, 195)-net over F₆₄, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
  2. digital (0, 4, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)
  3. digital (0, 9, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)
digital (54, 73, 932066)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁷³, 932066, F₆₄, 19, 19) (dual of [(932066, 19), 17709181, 20]-NRT-code), using
  - OOA 9-folding and stacking with additional row [i] based on linear OA(64⁷³, 8388595, F₆₄, 19) (dual of [8388595, 8388522, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁷³, large, F₆₄, 19) (dual of [large, large−73, 20]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

Mode: Constructive and linear.

None.

None.