MinT - Information on Result #2691951

Information on Result #2691951

Linear OOA(4¹⁷⁸, 157, F₄, 3, 62) (dual of [(157, 3), 293, 63]-NRT-code), using 4¹ times duplication based on linear OOA(4¹⁷⁷, 157, F₄, 3, 62) (dual of [(157, 3), 294, 63]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4⁴¹, 27, F₄, 3, 31) (dual of [(27, 3), 40, 32]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,49P) [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(4¹³⁶, 130, F₄, 3, 62) (dual of [(130, 3), 254, 63]-NRT-code), using
  - extracting embedded OOA [i] based on digital (74, 136, 130)-net over F₄, using
    - trace code for nets [i] based on digital (6, 68, 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.