MinT - Best Known (182−40, 182, s)-Nets in Base 2

Best Known (182−40, 182, s)-Nets in Base 2

(182−40, 182, 198)-Net over F₂ — Constructive and digital

Digital (142, 182, 198)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 20, 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 (122, 162, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 54, 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]

(182−40, 182, 364)-Net over F₂ — Digital

Digital (142, 182, 364)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−40, 182, 4527)-Net in Base 2 — Upper bound on s

There is no (142, 182, 4528)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 141064 925011 809691 261353 757640 267562 898884 994471 214266 > 2¹⁸² [i]