MinT - Best Known (140−37, 140, s)-Nets in Base 2

Best Known (140−37, 140, s)-Nets in Base 2

(140−37, 140, 135)-Net over F₂ — Constructive and digital

Digital (103, 140, 135)-net over F₂, using

1 times m-reduction [i] based on digital (103, 141, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 47, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(140−37, 140, 183)-Net over F₂ — Digital

Digital (103, 140, 183)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−37, 140, 1568)-Net in Base 2 — Upper bound on s

There is no (103, 140, 1569)-net in base 2, because

1 times m-reduction [i] would yield (103, 139, 1569)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 699567 475881 342250 263099 731438 323800 361384 > 2¹³⁹ [i]