MinT - Best Known (82−22, 82, s)-Nets in Base 2

Best Known (82−22, 82, s)-Nets in Base 2

(82−22, 82, 84)-Net over F₂ — Constructive and digital

Digital (60, 82, 84)-net over F₂, using

2¹ times duplication [i] based on digital (59, 81, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 27, 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]

(82−22, 82, 117)-Net over F₂ — Digital

Digital (60, 82, 117)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−22, 82, 845)-Net in Base 2 — Upper bound on s

There is no (60, 82, 846)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4 883058 616565 999533 449182 > 2⁸² [i]