MinT - Best Known (125−81, 125, s)-Nets in Base 2

Best Known (125−81, 125, s)-Nets in Base 2

(125−81, 125, 33)-Net over F₂ — Constructive and digital

Digital (44, 125, 33)-net over F₂, using

t-expansion [i] based on digital (39, 125, 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]

(125−81, 125, 34)-Net over F₂ — Digital

Digital (44, 125, 34)-net over F₂, using

t-expansion [i] based on digital (43, 125, 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]

(125−81, 125, 85)-Net in Base 2 — Upper bound on s

There is no (44, 125, 86)-net in base 2, because

1 times m-reduction [i] would yield (44, 124, 86)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25 297164 712141 049876 121511 955823 644700 > 2¹²⁴ [i]