MinT - Best Known (189−46, 189, s)-Nets in Base 2

Best Known (189−46, 189, s)-Nets in Base 2

(189−46, 189, 195)-Net over F₂ — Constructive and digital

Digital (143, 189, 195)-net over F₂, using

t-expansion [i] based on digital (142, 189, 195)-net over F₂, using
- 3 times m-reduction [i] based on digital (142, 192, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 64, 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]

(189−46, 189, 287)-Net over F₂ — Digital

Digital (143, 189, 287)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−46, 189, 2772)-Net in Base 2 — Upper bound on s

There is no (143, 189, 2773)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 787 800725 226041 467887 196397 348702 426130 958610 088979 456568 > 2¹⁸⁹ [i]