MinT - Best Known (86−26, 86, s)-Nets in Base 2

Best Known (86−26, 86, s)-Nets in Base 2

(86−26, 86, 66)-Net over F₂ — Constructive and digital

Digital (60, 86, 66)-net over F₂, using

4 times m-reduction [i] based on digital (60, 90, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 45, 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]

(86−26, 86, 91)-Net over F₂ — Digital

Digital (60, 86, 91)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−26, 86, 536)-Net in Base 2 — Upper bound on s

There is no (60, 86, 537)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 77 404729 543462 050342 827400 > 2⁸⁶ [i]