MinT - Best Known (54−37, 54, s)-Nets in Base 9

Best Known (54−37, 54, s)-Nets in Base 9

(54−37, 54, 74)-Net over F₉ — Constructive and digital

Digital (17, 54, 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]

(54−37, 54, 598)-Net in Base 9 — Upper bound on s

There is no (17, 54, 599)-net in base 9, because

1 times m-reduction [i] would yield (17, 53, 599)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 381 312218 884784 769027 016933 238946 356358 049055 442417 > 9⁵³ [i]