MinT - Information on Result #1792998

Information on Result #1792998

Digital (44, 94, 131)-net over F₈, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(8⁹⁴, 131, F₈, 3, 50) (dual of [(131, 3), 299, 51]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(8⁹⁴, 132, F₈, 3, 50) (dual of [(132, 3), 302, 51]-NRT-code), using
- constructionÂ X applied to AG(3;F,333P) âŠ‚ AG(3;F,340P) [i] based on
  1. linear OOA(8⁸⁸, 128, F₈, 3, 50) (dual of [(128, 3), 296, 51]-NRT-code), using algebraic-geometric NRT-code AG(3;F,333P) [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(8⁸¹, 128, F₈, 3, 43) (dual of [(128, 3), 303, 44]-NRT-code), using algebraic-geometric NRT-code AG(3;F,340P) [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129 (see above)
  3. linear OOA(8⁶, 4, F₈, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁶, 8, F₈, 3, 6) (dual of [(8, 3), 18, 7]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;18,8) [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.