MinT - Information on Result #1814689

Information on Result #1814689

Digital (18, 51, 578)-net over F₂₅₆, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁵¹, 578, F₂₅₆, 6, 33) (dual of [(578, 6), 3417, 34]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(256¹⁷, 289, F₂₅₆, 6, 16) (dual of [(289, 6), 1717, 17]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(6;F,1717P) [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(256³⁴, 289, F₂₅₆, 6, 33) (dual of [(289, 6), 1700, 34]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(6;F,1700P) [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.