MinT - Best Known (161, 161+58, s)-Nets in Base 2

Best Known (161, 161+58, s)-Nets in Base 2

(161, 161+58, 195)-Net over F₂ — Constructive and digital

Digital (161, 219, 195)-net over F₂, using

t-expansion [i] based on digital (160, 219, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 73, 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]

(161, 161+58, 260)-Net over F₂ — Digital

Digital (161, 219, 260)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+58, 2147)-Net in Base 2 — Upper bound on s

There is no (161, 219, 2148)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 850928 589877 526267 126224 057185 923942 917978 754248 105257 478115 993688 > 2²¹⁹ [i]