MinT - Best Known (105−24, 105, s)-Nets in Base 2

Best Known (105−24, 105, s)-Nets in Base 2

(105−24, 105, 144)-Net over F₂ — Constructive and digital

Digital (81, 105, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 35, 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]

(105−24, 105, 215)-Net over F₂ — Digital

Digital (81, 105, 215)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−24, 105, 2259)-Net in Base 2 — Upper bound on s

There is no (81, 105, 2260)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 40 646731 235026 943020 434186 039908 > 2¹⁰⁵ [i]