MinT - Best Known (234−94, 234, s)-Nets in Base 2

Best Known (234−94, 234, s)-Nets in Base 2

(234−94, 234, 75)-Net over F₂ — Constructive and digital

Digital (140, 234, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 86, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 148, 42)-net over F₂, using
  - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [i]

(234−94, 234, 105)-Net over F₂ — Digital

Digital (140, 234, 105)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−94, 234, 512)-Net in Base 2 — Upper bound on s

There is no (140, 234, 513)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 27937 687221 701983 650898 130926 665649 513719 032705 888964 647334 985859 416064 > 2²³⁴ [i]