MinT - Best Known (9, 54, s)-Nets in Base 25

Best Known (9, 54, s)-Nets in Base 25

(9, 54, 104)-Net over F₂₅ — Constructive and digital

Digital (9, 54, 104)-net over F₂₅, using

net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
  - a function field by GarcÃa and Quoos [i]

(9, 54, 868)-Net in Base 25 — Upper bound on s

There is no (9, 54, 869)-net in base 25, because

1 times m-reduction [i] would yield (9, 53, 869)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 124 925666 258128 835055 142861 364717 334753 127472 012058 910703 423168 754366 904465 > 25⁵³ [i]