MinT - Information on Result #1810596

Information on Result #1810596

Digital (15, 42, 128)-net over F₄₉, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(49⁴², 128, F₄₉, 3, 27) (dual of [(128, 3), 342, 28]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(49¹⁴, 64, F₄₉, 3, 13) (dual of [(64, 3), 178, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,178P) [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64, using
    - sharp bound on the number of rational points on curves with genus 1 [i]
2. linear OOA(49²⁸, 64, F₄₉, 3, 27) (dual of [(64, 3), 164, 28]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,164P) [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64 (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.