MinT - Best Known (18, 18+20, s)-Nets in Base 9

Best Known (18, 18+20, s)-Nets in Base 9

(18, 18+20, 74)-Net over F₉ — Constructive and digital

Digital (18, 38, 74)-net over F₉, using

t-expansion [i] based on digital (17, 38, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(18, 18+20, 79)-Net over F₉ — Digital

Digital (18, 38, 79)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(18, 18+20, 2387)-Net in Base 9 — Upper bound on s

There is no (18, 38, 2388)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 827750 174840 228049 733530 615939 271873 > 9³⁸ [i]