MinT - Best Known (42, 42+70, s)-Nets in Base 2

Best Known (42, 42+70, s)-Nets in Base 2

(42, 42+70, 33)-Net over F₂ — Constructive and digital

Digital (42, 112, 33)-net over F₂, using

t-expansion [i] based on digital (39, 112, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(42, 42+70, 83)-Net in Base 2 — Upper bound on s

There is no (42, 112, 84)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5526 375907 667188 937953 335164 393150 > 2¹¹² [i]