MinT - Information on Result #1802383

Information on Result #1802383

Digital (44, 97, 227)-net over F₁₆, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(16⁹⁷, 227, F₁₆, 2, 53) (dual of [(227, 2), 357, 54]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(16⁹⁷, 228, F₁₆, 2, 53) (dual of [(228, 2), 359, 54]-NRT-code), using
- constructionÂ X applied to AG(2;F,394P) âŠ‚ AG(2;F,399P) [i] based on
  1. linear OOA(16⁹³, 224, F₁₆, 2, 53) (dual of [(224, 2), 355, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,394P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(16⁸⁸, 224, F₁₆, 2, 48) (dual of [(224, 2), 360, 49]-NRT-code), using algebraic-geometric NRT-code AG(2;F,399P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (see above)
  3. linear OOA(16⁴, 4, F₁₆, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16⁴, 16, F₁₆, 2, 4) (dual of [(16, 2), 28, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;28,16) [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.