MinT - Best Known (86, 86+35, s)-Nets in Base 2

Best Known (86, 86+35, s)-Nets in Base 2

(86, 86+35, 84)-Net over F₂ — Constructive and digital

Digital (86, 121, 84)-net over F₂, using

2¹ times duplication [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]

(86, 86+35, 130)-Net over F₂ — Digital

Digital (86, 121, 130)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+35, 932)-Net in Base 2 — Upper bound on s

There is no (86, 121, 933)-net in base 2, because

1 times m-reduction [i] would yield (86, 120, 933)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 348630 254772 357651 006699 511610 678180 > 2¹²⁰ [i]