MinT - Information on Result #3001329

Information on Result #3001329

Linear OOA(2¹⁸³, 76, F₂, 8, 59) (dual of [(76, 8), 425, 60]-NRT-code), using 2² times duplication based on linear OOA(2¹⁸¹, 76, F₂, 8, 59) (dual of [(76, 8), 427, 60]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁸, 34, F₂, 8, 29) (dual of [(34, 8), 204, 30]-NRT-code), using
  - extracting embedded OOA [i] based on digital (39, 68, 34)-net over F₂, using
    - trace code for nets [i] based on digital (5, 34, 17)-net over F₄, using
      - net from sequence [i] based on digital (5, 16)-sequence over F₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
        an explicitly constructive algebraic function field [i]
2. linear OOA(2¹¹³, 42, F₂, 8, 59) (dual of [(42, 8), 223, 60]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(8;F,276P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]
  - algebraic-geometric NRT-code AG(8;F,46P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [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.