MinT - Best Known (84, 84+36, s)-Nets in Base 2

Best Known (84, 84+36, s)-Nets in Base 2

(84, 84+36, 75)-Net over F₂ — Constructive and digital

Digital (84, 120, 75)-net over F₂, using

trace code for nets [i] based on digital (4, 40, 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]

(84, 84+36, 118)-Net over F₂ — Digital

Digital (84, 120, 118)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+36, 741)-Net in Base 2 — Upper bound on s

There is no (84, 120, 742)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 352379 516209 595218 946697 408194 494420 > 2¹²⁰ [i]