MinT - Information on Result #2693285

Information on Result #2693285

Linear OOA(4²²², 164, F₄, 3, 77) (dual of [(164, 3), 270, 78]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(4²¹⁹, 163, F₄, 3, 77) (dual of [(163, 3), 270, 78]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4⁵³, 33, F₄, 3, 38) (dual of [(33, 3), 46, 39]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,60P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(4¹⁶⁶, 130, F₄, 3, 77) (dual of [(130, 3), 224, 78]-NRT-code), using
  - extracting embedded OOA [i] based on digital (89, 166, 130)-net over F₄, using
    - trace code for nets [i] based on digital (6, 83, 65)-net over F₁₆, using
      - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [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.