MinT - Best Known (85, 85+34, s)-Nets in Base 2

Best Known (85, 85+34, s)-Nets in Base 2

(85, 85+34, 84)-Net over F₂ — Constructive and digital

Digital (85, 119, 84)-net over F₂, using

1 times m-reduction [i] based on digital (85, 120, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 40, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [i]

(85, 85+34, 132)-Net over F₂ — Digital

Digital (85, 119, 132)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+34, 893)-Net in Base 2 — Upper bound on s

There is no (85, 119, 894)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 665042 089212 295236 294817 404393 492047 > 2¹¹⁹ [i]