MinT - Best Known (197, 197+62, s)-Nets in Base 2

Best Known (197, 197+62, s)-Nets in Base 2

(197, 197+62, 198)-Net over F₂ — Constructive and digital

Digital (197, 259, 198)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 31, 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 (166, 228, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 76, 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]

(197, 197+62, 390)-Net over F₂ — Digital

Digital (197, 259, 390)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197, 197+62, 4019)-Net in Base 2 — Upper bound on s

There is no (197, 259, 4020)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 929784 254071 881792 251353 628570 300287 991283 514624 786933 694901 006840 809996 992200 > 2²⁵⁹ [i]