MinT - Best Known (140, 180, s)-Nets in Base 2

Best Known (140, 180, s)-Nets in Base 2

(140, 180, 196)-Net over F₂ — Constructive and digital

Digital (140, 180, 196)-net over F₂, using

trace code for nets [i] based on digital (5, 45, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(140, 180, 350)-Net over F₂ — Digital

Digital (140, 180, 350)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 180, 4222)-Net in Base 2 — Upper bound on s

There is no (140, 180, 4223)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 536639 827502 531503 694019 155605 264878 189443 601432 164181 > 2¹⁸⁰ [i]