MinT - Best Known (45−30, 45, s)-Nets in Base 9

Best Known (45−30, 45, s)-Nets in Base 9

(45−30, 45, 64)-Net over F₉ — Constructive and digital

Digital (15, 45, 64)-net over F₉, using

t-expansion [i] based on digital (13, 45, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(45−30, 45, 576)-Net in Base 9 — Upper bound on s

There is no (15, 45, 577)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 840357 678462 874421 714352 762765 460907 155129 > 9⁴⁵ [i]