MinT - Best Known (149, 149+47, s)-Nets in Base 2

Best Known (149, 149+47, s)-Nets in Base 2

(149, 149+47, 195)-Net over F₂ — Constructive and digital

Digital (149, 196, 195)-net over F₂, using

t-expansion [i] based on digital (148, 196, 195)-net over F₂, using
- 5 times m-reduction [i] based on digital (148, 201, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 67, 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]

(149, 149+47, 308)-Net over F₂ — Digital

Digital (149, 196, 308)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+47, 3328)-Net in Base 2 — Upper bound on s

There is no (149, 196, 3329)-net in base 2, because

1 times m-reduction [i] would yield (149, 195, 3329)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 50322 235035 662484 245699 968244 156332 210971 780801 000696 946688 > 2¹⁹⁵ [i]