MinT - Best Known (84, 84+22, s)-Nets in Base 2

Best Known (84, 84+22, s)-Nets in Base 2

(84, 84+22, 180)-Net over F₂ — Constructive and digital

Digital (84, 106, 180)-net over F₂, using

2² times duplication [i] based on digital (82, 104, 180)-net over F₂, using
- trace code for nets [i] based on digital (4, 26, 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]

(84, 84+22, 292)-Net over F₂ — Digital

Digital (84, 106, 292)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+22, 3891)-Net in Base 2 — Upper bound on s

There is no (84, 106, 3892)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 81 340810 206034 694525 438001 749462 > 2¹⁰⁶ [i]