MinT - Information on Result #1813889

Information on Result #1813889

Digital (23, 61, 390)-net over F₁₂₈, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁶¹, 390, F₁₂₈, 3, 38) (dual of [(390, 3), 1109, 39]-NRT-code), using

strength reduction [i] based on linear OOA(128⁶¹, 390, F₁₂₈, 3, 39) (dual of [(390, 3), 1109, 40]-NRT-code), using
- constructionÂ X applied to AG(3;F,1115P) âŠ‚ AG(3;F,1123P) [i] based on
  1. linear OOA(128⁵⁴, 385, F₁₂₈, 3, 39) (dual of [(385, 3), 1101, 40]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1115P) [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386, using
    - a curve from the manYPoints database [i]
  2. linear OOA(128⁴⁶, 385, F₁₂₈, 3, 31) (dual of [(385, 3), 1109, 32]-NRT-code), using algebraic-geometric NRT-code AG(3;F,1123P) [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386 (see above)
  3. linear OOA(128⁷, 5, F₁₂₈, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁷, 128, F₁₂₈, 3, 7) (dual of [(128, 3), 377, 8]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;377,128) [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.