MinT - Information on Result #1814723

Information on Result #1814723

Digital (19, 53, 578)-net over F₂₅₆, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁵³, 578, F₂₅₆, 5, 34) (dual of [(578, 5), 2837, 35]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(256¹⁸, 289, F₂₅₆, 5, 17) (dual of [(289, 5), 1427, 18]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,1427P) [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(256³⁵, 289, F₂₅₆, 5, 34) (dual of [(289, 5), 1410, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,1410P) [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.