MinT - Best Known (52−31, 52, s)-Nets in Base 2

Best Known (52−31, 52, s)-Nets in Base 2

(52−31, 52, 21)-Net over F₂ — Constructive and digital

Digital (21, 52, 21)-net over F₂, using

net from sequence [i] based on digital (21, 20)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
  - an explicitly constructive algebraic function field [i]

(52−31, 52, 48)-Net in Base 2 — Upper bound on s

There is no (21, 52, 49)-net in base 2, because

1 times m-reduction [i] would yield (21, 51, 49)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2478 810338 533376 > 2⁵¹ [i]