MinT - Best Known (163, 163+38, s)-Nets in Base 2

Best Known (163, 163+38, s)-Nets in Base 2

(163, 163+38, 270)-Net over F₂ — Constructive and digital

Digital (163, 201, 270)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 25, 10)-net over F₂, using
  - net from sequence [i] based on digital (6, 9)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
      - an explicitly constructive algebraic function field [i]
  - Niederreiterâ€“Xing sequence (PirÅ¡iÄ‡ implementation) with equidistant coordinate [i]
2. digital (138, 176, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 44, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(163, 163+38, 626)-Net over F₂ — Digital

Digital (163, 201, 626)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+38, 12100)-Net in Base 2 — Upper bound on s

There is no (163, 201, 12101)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 217809 327994 506933 585969 038646 789935 460640 033231 412548 219008 > 2²⁰¹ [i]