MinT - Best Known (166, 166+74, s)-Nets in Base 3

Best Known (166, 166+74, s)-Nets in Base 3

(166, 166+74, 228)-Net over F₃ — Constructive and digital

Digital (166, 240, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 80, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(166, 166+74, 477)-Net over F₃ — Digital

Digital (166, 240, 477)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166, 166+74, 9077)-Net in Base 3 — Upper bound on s

There is no (166, 240, 9078)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 231327 612823 498705 982659 452741 126843 048927 608269 987801 904092 404062 468277 452911 699561 408852 364887 987099 435555 197957 > 3²⁴⁰ [i]