MinT - Best Known (85, 85+31, s)-Nets in Base 2

Best Known (85, 85+31, s)-Nets in Base 2

(85, 85+31, 102)-Net over F₂ — Constructive and digital

Digital (85, 116, 102)-net over F₂, using

1 times m-reduction [i] based on digital (85, 117, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 39, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(85, 85+31, 154)-Net over F₂ — Digital

Digital (85, 116, 154)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+31, 1283)-Net in Base 2 — Upper bound on s

There is no (85, 116, 1284)-net in base 2, because

1 times m-reduction [i] would yield (85, 115, 1284)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 41861 813212 486441 597045 707853 800000 > 2¹¹⁵ [i]