MinT - Information on Result #1802417

Information on Result #1802417

Digital (54, 98, 646)-net over F₁₆, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(16⁹⁸, 646, F₁₆, 2, 44) (dual of [(646, 2), 1194, 45]-NRT-code), using

trace code [i] based on linear OOA(256⁴⁹, 323, F₂₅₆, 2, 44) (dual of [(323, 2), 597, 45]-NRT-code), using
- constructionÂ X applied to AG(2;F,595P) âŠ‚ AG(2;F,599P) [i] based on
  1. linear OOA(256⁴⁶, 320, F₂₅₆, 2, 44) (dual of [(320, 2), 594, 45]-NRT-code), using algebraic-geometric NRT-code AG(2;F,595P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
    - sharp bound on the number of rational points on curves with genus 2 [i]
  2. linear OOA(256⁴², 320, F₂₅₆, 2, 40) (dual of [(320, 2), 598, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,599P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321 (see above)
  3. linear OOA(256³, 3, F₂₅₆, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(256³, 256, F₂₅₆, 2, 3) (dual of [(256, 2), 509, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;509,256) [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.