MinT - Best Known (109, 109+44, s)-Nets in Base 2

Best Known (109, 109+44, s)-Nets in Base 2

(109, 109+44, 102)-Net over F₂ — Constructive and digital

Digital (109, 153, 102)-net over F₂, using

trace code for nets [i] based on digital (7, 51, 34)-net over F₈, using
- net from sequence [i] based on digital (7, 33)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(109, 109+44, 158)-Net over F₂ — Digital

Digital (109, 153, 158)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+44, 1090)-Net in Base 2 — Upper bound on s

There is no (109, 153, 1091)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11435 370617 023737 652887 027700 967257 565061 043728 > 2¹⁵³ [i]