MinT - Best Known (40−18, 40, s)-Nets in Base 2

Best Known (40−18, 40, s)-Nets in Base 2

(40−18, 40, 21)-Net over F₂ — Constructive and digital

Digital (22, 40, 21)-net over F₂, using

t-expansion [i] based on digital (21, 40, 21)-net over F₂, using
- net from sequence [i] based on digital (21, 20)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(40−18, 40, 23)-Net over F₂ — Digital

Digital (22, 40, 23)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(40−18, 40, 78)-Net in Base 2 — Upper bound on s

There is no (22, 40, 79)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 206180 978904 > 2⁴⁰ [i]