MinT - Best Known (30−21, 30, s)-Nets in Base 25

Best Known (30−21, 30, s)-Nets in Base 25

(30−21, 30, 104)-Net over F₂₅ — Constructive and digital

Digital (9, 30, 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]

(30−21, 30, 2132)-Net in Base 25 — Upper bound on s

There is no (9, 30, 2133)-net in base 25, because

1 times m-reduction [i] would yield (9, 29, 2133)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 34853 896796 096239 894709 886640 583157 159025 > 25²⁹ [i]