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

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

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

Digital (62, 84, 84)-net over F₂, using

t-expansion [i] based on digital (61, 84, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 28, 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]

(84−22, 84, 127)-Net over F₂ — Digital

Digital (62, 84, 127)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−22, 84, 960)-Net in Base 2 — Upper bound on s

There is no (62, 84, 961)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 19 369295 623270 141575 955776 > 2⁸⁴ [i]