MinT - Information on Result #981435

Information on Result #981435

Linear OOA(8¹³⁶, 200, F₈, 3, 45) (dual of [(200, 3), 464, 46]-NRT-code), using OOA 2-folding based on linear OOA(8¹³⁶, 400, F₈, 2, 45) (dual of [(400, 2), 664, 46]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8³², 46, F₈, 2, 22) (dual of [(46, 2), 60, 23]-NRT-code), using
  - extracting embedded OOA [i] based on digital (10, 32, 46)-net over F₈, using
    - net from sequence [i] based on digital (10, 45)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 45, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
2. linear OOA(8¹⁰⁴, 354, F₈, 2, 45) (dual of [(354, 2), 604, 46]-NRT-code), using
  - extracting embedded OOA [i] based on digital (59, 104, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 52, 177)-net over F₆₄, using
      - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [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.