MinT - Information on Result #2691533

Information on Result #2691533

Linear OOA(4¹⁶⁸, 157, F₄, 3, 58) (dual of [(157, 3), 303, 59]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁶⁷, 157, F₄, 3, 58) (dual of [(157, 3), 304, 59]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4³⁹, 27, F₄, 3, 29) (dual of [(27, 3), 42, 30]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,51P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(4¹²⁸, 130, F₄, 3, 58) (dual of [(130, 3), 262, 59]-NRT-code), using
  - extracting embedded OOA [i] based on digital (70, 128, 130)-net over F₄, using
    - trace code for nets [i] based on digital (6, 64, 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.