MinT - Best Known (139, 139+47, s)-Nets in Base 2

Best Known (139, 139+47, s)-Nets in Base 2

(139, 139+47, 195)-Net over F₂ — Constructive and digital

Digital (139, 186, 195)-net over F₂, using

t-expansion [i] based on digital (138, 186, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 62, 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]

(139, 139+47, 257)-Net over F₂ — Digital

Digital (139, 186, 257)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 139+47, 2453)-Net in Base 2 — Upper bound on s

There is no (139, 186, 2454)-net in base 2, because

1 times m-reduction [i] would yield (139, 185, 2454)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 49 115537 628124 835468 959346 423981 692048 932384 702974 009388 > 2¹⁸⁵ [i]