MinT - Best Known (171−40, 171, s)-Nets in Base 2

Best Known (171−40, 171, s)-Nets in Base 2

(171−40, 171, 195)-Net over F₂ — Constructive and digital

Digital (131, 171, 195)-net over F₂, using

t-expansion [i] based on digital (130, 171, 195)-net over F₂, using
- 3 times m-reduction [i] based on digital (130, 174, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 58, 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]

(171−40, 171, 292)-Net over F₂ — Digital

Digital (131, 171, 292)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−40, 171, 3083)-Net in Base 2 — Upper bound on s

There is no (131, 171, 3084)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3009 534527 890750 003253 571366 078176 441238 080127 626368 > 2¹⁷¹ [i]