MinT - Information on Result #1814852

Information on Result #1814852

Digital (21, 60, 566)-net over F₂₅₆, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁶⁰, 566, F₂₅₆, 6, 39) (dual of [(566, 6), 3336, 40]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁶⁰, 578, F₂₅₆, 6, 39) (dual of [(578, 6), 3408, 40]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256²⁰, 289, F₂₅₆, 6, 19) (dual of [(289, 6), 1714, 20]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(6;F,1714P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]
  2. linear OOA(256⁴⁰, 289, F₂₅₆, 6, 39) (dual of [(289, 6), 1694, 40]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(6;F,1694P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289 (see above)

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.