MinT - Information on Result #2775146

Information on Result #2775146

Linear OOA(3²¹⁶, 77, F₃, 4, 102) (dual of [(77, 4), 92, 103]-NRT-code), using strength reduction based on linear OOA(3²¹⁶, 77, F₃, 4, 103) (dual of [(77, 4), 92, 104]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁷⁸, 37, F₃, 4, 51) (dual of [(37, 4), 70, 52]-NRT-code), using
  - extracting embedded OOA [i] based on digital (27, 78, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
2. linear OOA(3¹³⁸, 40, F₃, 4, 103) (dual of [(40, 4), 22, 104]-NRT-code), using
  - constructionÂ X applied to AG(4;F,20P) âŠ‚ AG(4;F,25P) [i] based on
    1. linear OOA(3¹²⁹, 36, F₃, 4, 103) (dual of [(36, 4), 15, 104]-NRT-code), using algebraic-geometric NRT-code AG(4;F,20P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    2. linear OOA(3¹¹⁹, 36, F₃, 4, 93) (dual of [(36, 4), 25, 94]-NRT-code), using algebraic-geometric NRT-code AG(4;F,25P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    3. linear OOA(3⁹, 4, F₃, 4, 9) (dual of [(4, 4), 7, 10]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(4;7,3) [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.