MinT - Information on Result #1813848

Information on Result #1813848

Digital (22, 59, 388)-net over F₁₂₈, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128⁵⁹, 388, F₁₂₈, 4, 37) (dual of [(388, 4), 1493, 38]-NRT-code), using

strength reduction [i] based on linear OOA(128⁵⁹, 388, F₁₂₈, 4, 38) (dual of [(388, 4), 1493, 39]-NRT-code), using
- constructionÂ X applied to AG(4;F,1501P) âŠ‚ AG(4;F,1508P) [i] based on
  1. linear OOA(128⁵³, 385, F₁₂₈, 4, 38) (dual of [(385, 4), 1487, 39]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1501P) [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, 4, 31) (dual of [(385, 4), 1494, 32]-NRT-code), using algebraic-geometric NRT-code AG(4;F,1508P) [i] based on function field F/F₁₂₈ with g(F) = 15 and N(F) ≥ 386 (see above)
  3. linear OOA(128⁶, 3, F₁₂₈, 4, 6) (dual of [(3, 4), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁶, 128, F₁₂₈, 4, 6) (dual of [(128, 4), 506, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(4;506,128) [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.