MinT - Best Known (36−16, 36, s)-Nets in Base 3

Best Known (36−16, 36, s)-Nets in Base 3

(36−16, 36, 40)-Net over F₃ — Constructive and digital

Digital (20, 36, 40)-net over F₃, using

trace code for nets [i] based on digital (2, 18, 20)-net over F₉, using
- net from sequence [i] based on digital (2, 19)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
    - a function field by GarcÃa and Quoos [i]

(36−16, 36, 256)-Net in Base 3 — Upper bound on s

There is no (20, 36, 257)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 151693 318108 797345 > 3³⁶ [i]