MinT - Best Known (18, 18+72, s)-Nets in Base 9

Best Known (18, 18+72, s)-Nets in Base 9

(18, 18+72, 74)-Net over F₉ — Constructive and digital

Digital (18, 90, 74)-net over F₉, using

t-expansion [i] based on digital (17, 90, 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+72, 412)-Net in Base 9 — Upper bound on s

There is no (18, 90, 413)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 82 177880 266716 344488 960511 491154 785034 085746 442018 476000 195535 442674 090934 883042 134305 > 9⁹⁰ [i]