MinT - Best Known (140, 140+41, s)-Nets in Base 2

Best Known (140, 140+41, s)-Nets in Base 2

(140, 140+41, 195)-Net over F₂ — Constructive and digital

Digital (140, 181, 195)-net over F₂, using

8 times m-reduction [i] based on digital (140, 189, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 63, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(140, 140+41, 334)-Net over F₂ — Digital

Digital (140, 181, 334)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+41, 4222)-Net in Base 2 — Upper bound on s

There is no (140, 181, 4223)-net in base 2, because

1 times m-reduction [i] would yield (140, 180, 4223)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 536639 827502 531503 694019 155605 264878 189443 601432 164181 > 2¹⁸⁰ [i]