MinT - Best Known (184−45, 184, s)-Nets in Base 2

Best Known (184−45, 184, s)-Nets in Base 2

(184−45, 184, 195)-Net over F₂ — Constructive and digital

Digital (139, 184, 195)-net over F₂, using

t-expansion [i] based on digital (138, 184, 195)-net over F₂, using
- 2 times m-reduction [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]

(184−45, 184, 278)-Net over F₂ — Digital

Digital (139, 184, 278)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−45, 184, 2857)-Net in Base 2 — Upper bound on s

There is no (139, 184, 2858)-net in base 2, because

1 times m-reduction [i] would yield (139, 183, 2858)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12 305267 426630 015626 195809 503850 843156 347394 017373 103704 > 2¹⁸³ [i]