MinT - Best Known (22−13, 22, s)-Nets in Base 25

Best Known (22−13, 22, s)-Nets in Base 25

(22−13, 22, 104)-Net over F₂₅ — Constructive and digital

Digital (9, 22, 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]

(22−13, 22, 9742)-Net in Base 25 — Upper bound on s

There is no (9, 22, 9743)-net in base 25, because

1 times m-reduction [i] would yield (9, 21, 9743)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 227418 869030 908362 897729 878641 > 25²¹ [i]