MinT - Best Known (85, 85+33, s)-Nets in Base 2

Best Known (85, 85+33, s)-Nets in Base 2

(85, 85+33, 84)-Net over F₂ — Constructive and digital

Digital (85, 118, 84)-net over F₂, using

2 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+33, 139)-Net over F₂ — Digital

Digital (85, 118, 139)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+33, 1057)-Net in Base 2 — Upper bound on s

There is no (85, 118, 1058)-net in base 2, because

1 times m-reduction [i] would yield (85, 117, 1058)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 166852 791241 396138 987565 809240 363110 > 2¹¹⁷ [i]