MinT - Best Known (154−40, 154, s)-Nets in Base 2

Best Known (154−40, 154, s)-Nets in Base 2

(154−40, 154, 144)-Net over F₂ — Constructive and digital

Digital (114, 154, 144)-net over F₂, using

2¹ times duplication [i] based on digital (113, 153, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 51, 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]

(154−40, 154, 206)-Net over F₂ — Digital

Digital (114, 154, 206)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−40, 154, 1697)-Net in Base 2 — Upper bound on s

There is no (114, 154, 1698)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22966 415163 096353 082444 366673 406832 040976 556136 > 2¹⁵⁴ [i]