MinT - Best Known (85, 85+62, s)-Nets in Base 2

Best Known (85, 85+62, s)-Nets in Base 2

(85, 85+62, 54)-Net over F₂ — Constructive and digital

Digital (85, 147, 54)-net over F₂, using

3 times m-reduction [i] based on digital (85, 150, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 75, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(85, 85+62, 64)-Net over F₂ — Digital

Digital (85, 147, 64)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+62, 288)-Net in Base 2 — Upper bound on s

There is no (85, 147, 289)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 178 752641 892488 146918 884044 991595 047942 144000 > 2¹⁴⁷ [i]