MinT - Best Known (46−27, 46, s)-Nets in Base 2

Best Known (46−27, 46, s)-Nets in Base 2

(46−27, 46, 20)-Net over F₂ — Constructive and digital

Digital (19, 46, 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]

(46−27, 46, 45)-Net in Base 2 — Upper bound on s

There is no (19, 46, 46)-net in base 2, because

1 times m-reduction [i] would yield (19, 45, 46)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 37 536163 543663 > 2⁴⁵ [i]