MinT - Best Known (75, 75+30, s)-Nets in Base 2

Best Known (75, 75+30, s)-Nets in Base 2

(75, 75+30, 84)-Net over F₂ — Constructive and digital

Digital (75, 105, 84)-net over F₂, using

trace code for nets [i] based on digital (5, 35, 28)-net over F₈, using
- net from sequence [i] based on digital (5, 27)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]

(75, 75+30, 121)-Net over F₂ — Digital

Digital (75, 105, 121)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+30, 800)-Net in Base 2 — Upper bound on s

There is no (75, 105, 801)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 40 965527 995945 018828 974138 467328 > 2¹⁰⁵ [i]