MinT - Best Known (109, 109+38, s)-Nets in Base 2

Best Known (109, 109+38, s)-Nets in Base 2

(109, 109+38, 144)-Net over F₂ — Constructive and digital

Digital (109, 147, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 49, 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]

(109, 109+38, 201)-Net over F₂ — Digital

Digital (109, 147, 201)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+38, 1663)-Net in Base 2 — Upper bound on s

There is no (109, 147, 1664)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 179 263874 452337 338009 604468 185243 931145 547401 > 2¹⁴⁷ [i]