MinT - Best Known (146−34, 146, s)-Nets in Base 2

Best Known (146−34, 146, s)-Nets in Base 2

(146−34, 146, 195)-Net over F₂ — Constructive and digital

Digital (112, 146, 195)-net over F₂, using

1 times m-reduction [i] based on digital (112, 147, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 49, 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]

(146−34, 146, 260)-Net over F₂ — Digital

Digital (112, 146, 260)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−34, 146, 2737)-Net in Base 2 — Upper bound on s

There is no (112, 146, 2738)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 89 563956 995163 781303 093725 927129 443178 849429 > 2¹⁴⁶ [i]