MinT - Best Known (181, 181+74, s)-Nets in Base 2

Best Known (181, 181+74, s)-Nets in Base 2

(181, 181+74, 144)-Net over F₂ — Constructive and digital

Digital (181, 255, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 85, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(181, 181+74, 238)-Net over F₂ — Digital

Digital (181, 255, 238)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(181, 181+74, 1685)-Net in Base 2 — Upper bound on s

There is no (181, 255, 1686)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 58021 208400 739869 746986 642324 327032 180085 915263 192568 989554 753492 700707 000988 > 2²⁵⁵ [i]