MinT - Best Known (117−34, 117, s)-Nets in Base 2

Best Known (117−34, 117, s)-Nets in Base 2

(117−34, 117, 84)-Net over F₂ — Constructive and digital

Digital (83, 117, 84)-net over F₂, using

trace code for nets [i] based on digital (5, 39, 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]

(117−34, 117, 125)-Net over F₂ — Digital

Digital (83, 117, 125)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(117−34, 117, 822)-Net in Base 2 — Upper bound on s

There is no (83, 117, 823)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 169352 480043 849566 116421 679886 438008 > 2¹¹⁷ [i]