MinT - Best Known (80−18, 80, s)-Nets in Base 2

Best Known (80−18, 80, s)-Nets in Base 2

(80−18, 80, 132)-Net over F₂ — Constructive and digital

Digital (62, 80, 132)-net over F₂, using

trace code for nets [i] based on digital (2, 20, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]

(80−18, 80, 190)-Net over F₂ — Digital

Digital (62, 80, 190)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−18, 80, 1952)-Net in Base 2 — Upper bound on s

There is no (62, 80, 1953)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 208962 035632 043702 277688 > 2⁸⁰ [i]