MinT - Information on Result #1805663

Information on Result #1805663

Digital (46, 107, 289)-net over F₂₅, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(25¹⁰⁷, 289, F₂₅, 2, 61) (dual of [(289, 2), 471, 62]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(25¹⁰⁷, 292, F₂₅, 2, 61) (dual of [(292, 2), 477, 62]-NRT-code), using
- constructionÂ X applied to AG(2;F,512P) âŠ‚ AG(2;F,518P) [i] based on
  1. linear OOA(25¹⁰², 287, F₂₅, 2, 61) (dual of [(287, 2), 472, 62]-NRT-code), using algebraic-geometric NRT-code AG(2;F,512P) [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(25⁹⁶, 287, F₂₅, 2, 55) (dual of [(287, 2), 478, 56]-NRT-code), using algebraic-geometric NRT-code AG(2;F,518P) [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288 (see above)
  3. linear OOA(25⁵, 5, F₂₅, 2, 5) (dual of [(5, 2), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁵, 25, F₂₅, 2, 5) (dual of [(25, 2), 45, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;45,25) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.