MinT - Information on Result #1011375

Information on Result #1011375

Linear OOA(3¹⁸¹, 74, F₃, 3, 88) (dual of [(74, 3), 41, 89]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁷¹, 37, F₃, 3, 44) (dual of [(37, 3), 40, 45]-NRT-code), using
- extracting embedded OOA [i] based on digital (27, 71, 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, 88) (dual of [(37, 3), 1, 89]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹¹⁰, 38, F₃, 3, 88) (dual of [(38, 3), 4, 89]-NRT-code), using
  - strength reduction [i] based on linear OOA(3¹¹⁰, 38, F₃, 3, 90) (dual of [(38, 3), 4, 91]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3⁸, 4, F₃, 3, 8) (dual of [(4, 3), 4, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;4,3) [i]
      2. linear OOA(3⁹⁸, 34, F₃, 3, 81) (dual of [(34, 3), 4, 82]-NRT-code), using
        6 step truncation [i] based on linear OOA(3¹⁰⁴, 36, F₃, 3, 87) (dual of [(36, 3), 4, 88]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(9⁷, 9, F₉, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,9)), using
        Reedâ€“Solomon code RS(2,9) [i]
        linear OOA(3¹⁰, 4, F₃, 3, 10) (dual of [(4, 3), 2, 11]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;2,3) [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.