MinT - Information on Result #1811417

Information on Result #1811417

Digital (24, 59, 344)-net over F₆₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁵⁹, 344, F₆₄, 3, 35) (dual of [(344, 3), 973, 36]-NRT-code), using

constructionÂ X applied to AG(3;F,987P) âŠ‚ AG(3;F,992P) [i] based on
1. linear OOA(64⁵⁵, 341, F₆₄, 3, 35) (dual of [(341, 3), 968, 36]-NRT-code), using algebraic-geometric NRT-code AG(3;F,987P) [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
  - a curve from the manYPoints database [i]
2. linear OOA(64⁵⁰, 341, F₆₄, 3, 30) (dual of [(341, 3), 973, 31]-NRT-code), using algebraic-geometric NRT-code AG(3;F,992P) [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342 (see above)
3. linear OOA(64⁴, 3, F₆₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 3, 4) (dual of [(64, 3), 188, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;188,64) [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.