MinT - Information on Result #1813414

Information on Result #1813414

Digital (12, 31, 322)-net over F₁₂₈, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(128³¹, 322, F₁₂₈, 2, 19) (dual of [(322, 2), 613, 20]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(128¹⁰, 150, F₁₂₈, 2, 9) (dual of [(150, 2), 290, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,290P) [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]
2. linear OOA(128²¹, 172, F₁₂₈, 2, 19) (dual of [(172, 2), 323, 20]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,324P) [i] based on function field F/F₁₂₈ with g(F) = 2 and N(F) ≥ 172, using
    - sharp bound on the number of rational points on curves with genus 2 [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.