MinT - Information on Result #1229658

Information on Result #1229658

Digital (56, 78, 226)-net over F₇, using generalized (u,Â u+v)-construction based on

digital (5, 12, 26)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 4, 50)-net over F₇, using
    - net defined by OOA [i] based on linear OOA(7⁴, 50, F₇, 3, 3) (dual of [(50, 3), 146, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(7⁴, 50, F₇, 2, 3) (dual of [(50, 2), 96, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7⁴, 50, F₇, 3) (dual of [50, 46, 4]-code or 50-cap in PG(3,7)), using
        ovoid in PG(3,Â 7) [i]
  2. digital (1, 8, 13)-net over F₇, using
    - 5 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
digital (11, 22, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 11, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
      - the rational function field F₄₉(x) [i]
    - Niederreiter sequence [i]
digital (22, 44, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 22, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

Mode: Constructive and linear.

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