MinT - Best Known (36−14, 36, s)-Nets in Base 3

Best Known (36−14, 36, s)-Nets in Base 3

(36−14, 36, 60)-Net over F₃ — Constructive and digital

Digital (22, 36, 60)-net over F₃, using

trace code for nets [i] based on digital (4, 18, 30)-net over F₉, using
- net from sequence [i] based on digital (4, 29)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
    - a function field by SÃ©mirat [i]

(36−14, 36, 473)-Net in Base 3 — Upper bound on s

There is no (22, 36, 474)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 150106 969249 847817 > 3³⁶ [i]