MinT - Best Known (51−31, 51, s)-Nets in Base 2

Best Known (51−31, 51, s)-Nets in Base 2

(51−31, 51, 20)-Net over F₂ — Constructive and digital

Digital (20, 51, 20)-net over F₂, using

t-expansion [i] based on digital (19, 51, 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]

(51−31, 51, 45)-Net in Base 2 — Upper bound on s

There is no (20, 51, 46)-net in base 2, because

1 times m-reduction [i] would yield (20, 50, 46)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1230 185577 016156 > 2⁵⁰ [i]