MinT - Information on Result #1811398

Information on Result #1811398

Digital (24, 58, 345)-net over F₆₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(64⁵⁸, 345, F₆₄, 2, 34) (dual of [(345, 2), 632, 35]-NRT-code), using

constructionÂ X applied to AG(2;F,647P) âŠ‚ AG(2;F,652P) [i] based on
1. linear OOA(64⁵⁴, 341, F₆₄, 2, 34) (dual of [(341, 2), 628, 35]-NRT-code), using algebraic-geometric NRT-code AG(2;F,647P) [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(64⁴⁹, 341, F₆₄, 2, 29) (dual of [(341, 2), 633, 30]-NRT-code), using algebraic-geometric NRT-code AG(2;F,652P) [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342 (see above)
3. linear OOA(64⁴, 4, F₆₄, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 2, 4) (dual of [(64, 2), 124, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;124,64) [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.