MinT - Best Known (185, 185+54, s)-Nets in Base 2

Best Known (185, 185+54, s)-Nets in Base 2

(185, 185+54, 206)-Net over F₂ — Constructive and digital

Digital (185, 239, 206)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 35, 11)-net over F₂, using
  - net from sequence [i] based on digital (8, 10)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 8 and N(F) ≥ 11, using
      - an explicitly constructive algebraic function field [i]
2. 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]

(185, 185+54, 425)-Net over F₂ — Digital

Digital (185, 239, 425)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(185, 185+54, 5007)-Net in Base 2 — Upper bound on s

There is no (185, 239, 5008)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 884920 262260 515689 366295 813767 354509 867930 729652 902063 316069 888872 752136 > 2²³⁹ [i]