MinT - Information on Result #1810294

Information on Result #1810294

Digital (7, 18, 128)-net over F₄₉, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(49¹⁸, 128, F₄₉, 11) (dual of [128, 110, 12]-code), using

(u,Â u+v)-construction [i] based on
1. linear OA(49⁶, 64, F₄₉, 5) (dual of [64, 58, 6]-code), using
  - extended algebraic-geometric code AG_e(F,58P) [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 OA(49¹², 64, F₄₉, 11) (dual of [64, 52, 12]-code), using
  - extended algebraic-geometric code AG_e(F,52P) [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.