MinT - Information on Result #2855807

Information on Result #2855807

Linear OOA(3²⁰⁹, 75, F₃, 5, 100) (dual of [(75, 5), 166, 101]-NRT-code), using strength reduction based on linear OOA(3²⁰⁹, 75, F₃, 5, 101) (dual of [(75, 5), 166, 102]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁷⁷, 37, F₃, 5, 50) (dual of [(37, 5), 108, 51]-NRT-code), using
  - extracting embedded OOA [i] based on digital (27, 77, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. linear OOA(3¹³², 38, F₃, 5, 101) (dual of [(38, 5), 58, 102]-NRT-code), using
  - constructionÂ X applied to AG(5;F,39P) âŠ‚ AG(5;F,42P) [i] based on
    1. linear OOA(3¹²⁷, 36, F₃, 5, 101) (dual of [(36, 5), 53, 102]-NRT-code), using algebraic-geometric NRT-code AG(5;F,39P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    2. linear OOA(3¹²¹, 36, F₃, 5, 95) (dual of [(36, 5), 59, 96]-NRT-code), using algebraic-geometric NRT-code AG(5;F,42P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    3. linear OOA(3⁵, 2, F₃, 5, 5) (dual of [(2, 5), 5, 6]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3⁵, 3, F₃, 5, 5) (dual of [(3, 5), 10, 6]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(5;10,3) [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.