MinT - Best Known (198−54, 198, s)-Nets in Base 2

Best Known (198−54, 198, s)-Nets in Base 2

(198−54, 198, 144)-Net over F₂ — Constructive and digital

Digital (144, 198, 144)-net over F₂, using

t-expansion [i] based on digital (143, 198, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 66, 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]

(198−54, 198, 222)-Net over F₂ — Digital

Digital (144, 198, 222)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−54, 198, 1722)-Net in Base 2 — Upper bound on s

There is no (144, 198, 1723)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 406539 365178 841255 627164 174503 316384 955315 207386 643428 580610 > 2¹⁹⁸ [i]