MinT - Best Known (18−8, 18, s)-Nets in Base 9

Best Known (18−8, 18, s)-Nets in Base 9

(18−8, 18, 200)-Net over F₉ — Constructive and digital

Digital (10, 18, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 9, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(18−8, 18, 5443)-Net in Base 9 — Upper bound on s

There is no (10, 18, 5444)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 150127 125173 630849 > 9¹⁸ [i]