MinT - Best Known (19, 57, s)-Nets in Base 2

Best Known (19, 57, s)-Nets in Base 2

(19, 57, 20)-Net over F₂ — Constructive and digital

Digital (19, 57, 20)-net over F₂, using

net from sequence [i] based on digital (19, 19)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
  - an explicitly constructive algebraic function field [i]

(19, 57, 40)-Net in Base 2 — Upper bound on s

There is no (19, 57, 41)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 196042 634824 197648 > 2⁵⁷ [i]