MinT - Information on Result #1805548

Information on Result #1805548

Digital (45, 104, 291)-net over F₂₅, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(25¹⁰⁴, 291, F₂₅, 2, 59) (dual of [(291, 2), 478, 60]-NRT-code), using

constructionÂ X applied to AG(2;F,514P) âŠ‚ AG(2;F,519P) [i] based on
1. linear OOA(25¹⁰⁰, 287, F₂₅, 2, 59) (dual of [(287, 2), 474, 60]-NRT-code), using algebraic-geometric NRT-code AG(2;F,514P) [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(25⁹⁵, 287, F₂₅, 2, 54) (dual of [(287, 2), 479, 55]-NRT-code), using algebraic-geometric NRT-code AG(2;F,519P) [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288 (see above)
3. linear OOA(25⁴, 4, F₂₅, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(25⁴, 25, F₂₅, 2, 4) (dual of [(25, 2), 46, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;46,25) [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.