MinT - Best Known (54−14, 54, s)-Nets in Base 2

Best Known (54−14, 54, s)-Nets in Base 2

(54−14, 54, 75)-Net over F₂ — Constructive and digital

Digital (40, 54, 75)-net over F₂, using

trace code for nets [i] based on digital (4, 18, 25)-net over F₈, using
- net from sequence [i] based on digital (4, 24)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
    - a function field by SÃ©mirat [i]

(54−14, 54, 100)-Net over F₂ — Digital

Digital (40, 54, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−14, 54, 699)-Net in Base 2 — Upper bound on s

There is no (40, 54, 700)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 18034 922742 557066 > 2⁵⁴ [i]