MinT - Best Known (78−22, 78, s)-Nets in Base 2

Best Known (78−22, 78, s)-Nets in Base 2

(78−22, 78, 75)-Net over F₂ — Constructive and digital

Digital (56, 78, 75)-net over F₂, using

trace code for nets [i] based on digital (4, 26, 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]

(78−22, 78, 100)-Net over F₂ — Digital

Digital (56, 78, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−22, 78, 653)-Net in Base 2 — Upper bound on s

There is no (56, 78, 654)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 305111 248549 309452 050510 > 2⁷⁸ [i]