MinT - Best Known (42, 42+40, s)-Nets in Base 2

Best Known (42, 42+40, s)-Nets in Base 2

(42, 42+40, 33)-Net over F₂ — Constructive and digital

Digital (42, 82, 33)-net over F₂, using

t-expansion [i] based on digital (39, 82, 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+40, 98)-Net in Base 2 — Upper bound on s

There is no (42, 82, 99)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁸², 99, S₂, 40), but
- the linear programming bound shows that MÂ â‰¥ 9903 520314 283042 199192 993792 / 1885 > 2⁸² [i]