MinT - Best Known (41, 41+53, s)-Nets in Base 2

Best Known (41, 41+53, s)-Nets in Base 2

(41, 41+53, 33)-Net over F₂ — Constructive and digital

Digital (41, 94, 33)-net over F₂, using

t-expansion [i] based on digital (39, 94, 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]

(41, 41+53, 92)-Net in Base 2 — Upper bound on s

There is no (41, 94, 93)-net in base 2, because

1 times m-reduction [i] would yield (41, 93, 93)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12168 084073 270753 875964 678430 > 2⁹³ [i]