MinT - Best Known (67, 67+32, s)-Nets in Base 2

Best Known (67, 67+32, s)-Nets in Base 2

(67, 67+32, 66)-Net over F₂ — Constructive and digital

Digital (67, 99, 66)-net over F₂, using

5 times m-reduction [i] based on digital (67, 104, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 52, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(67, 67+32, 86)-Net over F₂ — Digital

Digital (67, 99, 86)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+32, 472)-Net in Base 2 — Upper bound on s

There is no (67, 99, 473)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 641499 629759 866278 428950 339659 > 2⁹⁹ [i]