MinT - Best Known (232−66, 232, s)-Nets in Base 2

Best Known (232−66, 232, s)-Nets in Base 2

(232−66, 232, 144)-Net over F₂ — Constructive and digital

Digital (166, 232, 144)-net over F₂, using

2¹ times duplication [i] based on digital (165, 231, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 77, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(232−66, 232, 230)-Net over F₂ — Digital

Digital (166, 232, 230)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−66, 232, 1672)-Net in Base 2 — Upper bound on s

There is no (166, 232, 1673)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7001 187569 864699 181729 884144 965905 012569 246437 205167 854085 667793 370584 > 2²³² [i]