MinT - Information on Result #1792846

Information on Result #1792846

Digital (42, 89, 130)-net over F₈, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(8⁸⁹, 130, F₈, 3, 47) (dual of [(130, 3), 301, 48]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(8⁸⁹, 131, F₈, 3, 47) (dual of [(131, 3), 304, 48]-NRT-code), using
- constructionÂ X applied to AG(3;F,336P) âŠ‚ AG(3;F,341P) [i] based on
  1. linear OOA(8⁸⁵, 128, F₈, 3, 47) (dual of [(128, 3), 299, 48]-NRT-code), using algebraic-geometric NRT-code AG(3;F,336P) [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]
  2. linear OOA(8⁸⁰, 128, F₈, 3, 42) (dual of [(128, 3), 304, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,341P) [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129 (see above)
  3. linear OOA(8⁴, 3, F₈, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;20,8) [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.