MinT - Best Known (69−16, 69, s)-Nets in Base 2

Best Known (69−16, 69, s)-Nets in Base 2

(69−16, 69, 102)-Net over F₂ — Constructive and digital

Digital (53, 69, 102)-net over F₂, using

trace code for nets [i] based on digital (7, 23, 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]

(69−16, 69, 159)-Net over F₂ — Digital

Digital (53, 69, 159)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(69−16, 69, 1474)-Net in Base 2 — Upper bound on s

There is no (53, 69, 1475)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 591 162608 104132 790696 > 2⁶⁹ [i]