MinT - Information on Result #1093629

Information on Result #1093629

Linear OOA(3²¹⁷, 78, F₃, 4, 102) (dual of [(78, 4), 95, 103]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁷⁸, 37, F₃, 4, 51) (dual of [(37, 4), 70, 52]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 78, 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]
linear OOA(3¹³⁹, 41, F₃, 4, 102) (dual of [(41, 4), 25, 103]-NRT-code), using
- strength reduction [i] based on linear OOA(3¹³⁹, 41, F₃, 4, 103) (dual of [(41, 4), 25, 104]-NRT-code), using
  - constructionÂ X applied to AG(4;F,20P) âŠ‚ AG(4;F,25P) [i] based on
    1. linear OOA(3¹²⁹, 36, F₃, 4, 103) (dual of [(36, 4), 15, 104]-NRT-code), using algebraic-geometric NRT-code AG(4;F,20P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    2. linear OOA(3¹¹⁹, 36, F₃, 4, 93) (dual of [(36, 4), 25, 94]-NRT-code), using algebraic-geometric NRT-code AG(4;F,25P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    3. linear OOA(3¹⁰, 5, F₃, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3¹⁰, 7, F₃, 4, 9) (dual of [(7, 4), 18, 10]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,18P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [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.