MinT - Best Known (86, 86+23, s)-Nets in Base 2

Best Known (86, 86+23, s)-Nets in Base 2

(86, 86+23, 180)-Net over F₂ — Constructive and digital

Digital (86, 109, 180)-net over F₂, using

2¹ times duplication [i] based on digital (85, 108, 180)-net over F₂, using
- trace code for nets [i] based on digital (4, 27, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(86, 86+23, 281)-Net over F₂ — Digital

Digital (86, 109, 281)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+23, 4415)-Net in Base 2 — Upper bound on s

There is no (86, 109, 4416)-net in base 2, because

1 times m-reduction [i] would yield (86, 108, 4416)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 324 648675 891504 810878 924288 782953 > 2¹⁰⁸ [i]