MinT - Best Known (137, 175, s)-Nets in Base 2

Best Known (137, 175, s)-Nets in Base 2

(137, 175, 198)-Net over F₂ — Constructive and digital

Digital (137, 175, 198)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 19, 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 (118, 156, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 52, 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]

(137, 175, 365)-Net over F₂ — Digital

Digital (137, 175, 365)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 175, 4669)-Net in Base 2 — Upper bound on s

There is no (137, 175, 4670)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 47986 558363 939393 499196 864182 340734 962506 800417 142558 > 2¹⁷⁵ [i]