MinT - Best Known (140, 140+50, s)-Nets in Base 2

Best Known (140, 140+50, s)-Nets in Base 2

(140, 140+50, 144)-Net over F₂ — Constructive and digital

Digital (140, 190, 144)-net over F₂, using

t-expansion [i] based on digital (139, 190, 144)-net over F₂, using
- 2 times m-reduction [i] based on digital (139, 192, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 64, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]

(140, 140+50, 235)-Net over F₂ — Digital

Digital (140, 190, 235)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+50, 1937)-Net in Base 2 — Upper bound on s

There is no (140, 190, 1938)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1573 287313 739004 444808 835669 608103 870228 047062 223085 581264 > 2¹⁹⁰ [i]