MinT - Best Known (151, 151+46, s)-Nets in Base 2

Best Known (151, 151+46, s)-Nets in Base 2

(151, 151+46, 195)-Net over F₂ — Constructive and digital

Digital (151, 197, 195)-net over F₂, using

t-expansion [i] based on digital (150, 197, 195)-net over F₂, using
- 7 times m-reduction [i] based on digital (150, 204, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 68, 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]

(151, 151+46, 330)-Net over F₂ — Digital

Digital (151, 197, 330)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+46, 3537)-Net in Base 2 — Upper bound on s

There is no (151, 197, 3538)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 201399 252122 386695 191691 739931 777412 237190 237443 233124 348512 > 2¹⁹⁷ [i]