MinT - Best Known (116−73, 116, s)-Nets in Base 2

Best Known (116−73, 116, s)-Nets in Base 2

(116−73, 116, 33)-Net over F₂ — Constructive and digital

Digital (43, 116, 33)-net over F₂, using

t-expansion [i] based on digital (39, 116, 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]

(116−73, 116, 34)-Net over F₂ — Digital

Digital (43, 116, 34)-net over F₂, using

net from sequence [i] based on digital (43, 33)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 43 and N(F) ≥ 34, using
  - a curve from the manYPoints database [i]

(116−73, 116, 85)-Net in Base 2 — Upper bound on s

There is no (43, 116, 86)-net in base 2, because

1 times m-reduction [i] would yield (43, 115, 86)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 48415 080473 139085 125978 629899 821730 > 2¹¹⁵ [i]