MinT - Information on Result #1011338

Information on Result #1011338

Linear OOA(3¹⁷⁹, 74, F₃, 3, 84) (dual of [(74, 3), 43, 85]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁹, 37, F₃, 3, 42) (dual of [(37, 3), 42, 43]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 69, 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(3¹¹⁰, 37, F₃, 3, 84) (dual of [(37, 3), 1, 85]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹¹⁰, 39, F₃, 3, 84) (dual of [(39, 3), 7, 85]-NRT-code), using
  - strength reduction [i] based on linear OOA(3¹¹⁰, 39, F₃, 3, 85) (dual of [(39, 3), 7, 86]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3²⁶, 11, F₃, 3, 22) (dual of [(11, 3), 7, 23]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(3²⁶, 12, F₃, 3, 22) (dual of [(12, 3), 10, 23]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(3⁷⁷, 28, F₃, 3, 62) (dual of [(28, 3), 7, 63]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,21P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, 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.