MinT - Information on Result #1013879

Information on Result #1013879

Linear OOA(7³⁴, 121, F₇, 3, 12) (dual of [(121, 3), 329, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7¹⁰, 21, F₇, 3, 6) (dual of [(21, 3), 53, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7³, 8, F₇, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;21,7) [i]
  2. linear OOA(7⁷, 13, F₇, 3, 6) (dual of [(13, 3), 32, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 7, 13)-net over F₇, using
      - 6 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
linear OOA(7²⁴, 100, F₇, 3, 12) (dual of [(100, 3), 276, 13]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 24, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 12, 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]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.