MinT - Information on Result #1801334

Information on Result #1801334

Digital (22, 49, 131)-net over F₁₆, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(16⁴⁹, 131, F₁₆, 2, 27) (dual of [(131, 2), 213, 28]-NRT-code), using

constructionÂ X applied to AG(2;F,228P) âŠ‚ AG(2;F,232P) [i] based on
1. linear OOA(16⁴⁶, 128, F₁₆, 2, 27) (dual of [(128, 2), 210, 28]-NRT-code), using algebraic-geometric NRT-code AG(2;F,228P) [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]
2. linear OOA(16⁴², 128, F₁₆, 2, 23) (dual of [(128, 2), 214, 24]-NRT-code), using algebraic-geometric NRT-code AG(2;F,232P) [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129 (see above)
3. linear OOA(16³, 3, F₁₆, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16³, 16, F₁₆, 2, 3) (dual of [(16, 2), 29, 4]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;29,16) [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.