MinT - Best Known (42, 42+28, s)-Nets in Base 2

Best Known (42, 42+28, s)-Nets in Base 2

(42, 42+28, 42)-Net over F₂ — Constructive and digital

Digital (42, 70, 42)-net over F₂, using

trace code for nets [i] based on digital (7, 35, 21)-net over F₄, using
- net from sequence [i] based on digital (7, 20)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(42, 42+28, 173)-Net in Base 2 — Upper bound on s

There is no (42, 70, 174)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1189 475045 753223 656712 > 2⁷⁰ [i]