MinT - Information on Result #1049052

Information on Result #1049052

Linear OOA(4²¹⁰, 166, F₄, 3, 71) (dual of [(166, 3), 288, 72]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4⁵⁶, 36, F₄, 3, 35) (dual of [(36, 3), 52, 36]-NRT-code), using
- constructionÂ X applied to AG(3;F,60P) âŠ‚ AG(3;F,67P) [i] based on
  1. linear OOA(4⁵⁰, 32, F₄, 3, 35) (dual of [(32, 3), 46, 36]-NRT-code), using algebraic-geometric NRT-code AG(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(4⁴³, 32, F₄, 3, 28) (dual of [(32, 3), 53, 29]-NRT-code), using algebraic-geometric NRT-code AG(3;F,67P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
  3. linear OOA(4⁶, 4, F₄, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;6,4) [i]
linear OOA(4¹⁵⁴, 130, F₄, 3, 71) (dual of [(130, 3), 236, 72]-NRT-code), using
- extracting embedded OOA [i] based on digital (83, 154, 130)-net over F₄, using
  - trace code for nets [i] based on digital (6, 77, 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.