MinT - Information on Result #1229583

Information on Result #1229583

Digital (61, 83, 232)-net over F₇, using generalized (u,Â u+v)-construction based on

digital (2, 7, 16)-net over F₇, using
- s-reduction based on digital (2, 7, 21)-net over F₇, using
  - net defined by OOA [i] based on linear OOA(7⁷, 21, F₇, 5, 5) (dual of [(21, 5), 98, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(7⁷, 43, F₇, 5) (dual of [43, 36, 6]-code), using
      - a code by Danev and Olsson [i]
digital (3, 10, 16)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 8)-net over F₇, using
    - net from sequence [i] based on digital (0, 7)-sequence over F₇, using
      - Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using
        the rational function field F₇(x) [i]
      - Niederreiter sequence [i]
  2. digital (0, 7, 8)-net over F₇, using
    - net from sequence [i] based on digital (0, 7)-sequence over F₇ (see above)
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.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.