MinT - Information on Result #1810713

Information on Result #1810713

Digital (17, 48, 128)-net over F₄₉, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(49⁴⁸, 128, F₄₉, 2, 31) (dual of [(128, 2), 208, 32]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(49¹⁶, 64, F₄₉, 2, 15) (dual of [(64, 2), 112, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,112P) [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(49³², 64, F₄₉, 2, 31) (dual of [(64, 2), 96, 32]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,96P) [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.