MinT - Best Known (141, 141+40, s)-Nets in Base 2

Best Known (141, 141+40, s)-Nets in Base 2

(141, 141+40, 196)-Net over F₂ — Constructive and digital

Digital (141, 181, 196)-net over F₂, using

2¹ times duplication [i] based on 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]

(141, 141+40, 357)-Net over F₂ — Digital

Digital (141, 181, 357)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+40, 4372)-Net in Base 2 — Upper bound on s

There is no (141, 181, 4373)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 073870 860594 532966 405011 906706 684302 107345 505645 732401 > 2¹⁸¹ [i]