MinT - Information on Result #1013975

Information on Result #1013975

Linear OOA(7⁴⁵, 121, F₇, 3, 16) (dual of [(121, 3), 318, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7¹³, 21, F₇, 3, 8) (dual of [(21, 3), 50, 9]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁴, 8, F₇, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;20,7) [i]
  2. linear OOA(7⁹, 13, F₇, 3, 8) (dual of [(13, 3), 30, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 9, 13)-net over F₇, using
      - 4 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
linear OOA(7³², 100, F₇, 3, 16) (dual of [(100, 3), 268, 17]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 32, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 16, 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.