MinT - Best Known (184, 184+57, s)-Nets in Base 2

Best Known (184, 184+57, s)-Nets in Base 2

(184, 184+57, 198)-Net over F₂ — Constructive and digital

Digital (184, 241, 198)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 28, 3)-net over F₂, using
  - net from sequence [i] based on digital (0, 2)-sequence over F₂, using
    - Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 0 and N(F) ≥ 3, using
      - the rational function field F₂(x) [i]
    - Niederreiter sequence [i]
    - Sobol sequence [i]
2. digital (156, 213, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 71, 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, 184+57, 380)-Net over F₂ — Digital

Digital (184, 241, 380)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(184, 184+57, 4256)-Net in Base 2 — Upper bound on s

There is no (184, 241, 4257)-net in base 2, because

1 times m-reduction [i] would yield (184, 240, 4257)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 770994 374580 105442 171016 227389 814052 764166 175587 465178 969078 681433 259480 > 2²⁴⁰ [i]