MinT - Best Known (19, 52, s)-Nets in Base 25

Best Known (19, 52, s)-Nets in Base 25

(19, 52, 148)-Net over F₂₅ — Constructive and digital

Digital (19, 52, 148)-net over F₂₅, using

net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
  - a function field by GarcÃa and Quoos [i]

(19, 52, 162)-Net over F₂₅ — Digital

Digital (19, 52, 162)-net over F₂₅, using

net from sequence [i] based on digital (19, 161)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 162, using
  - an algebraic function field by Teo [i]

(19, 52, 8087)-Net in Base 25 — Upper bound on s

There is no (19, 52, 8088)-net in base 25, because

1 times m-reduction [i] would yield (19, 51, 8088)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 197346 593478 838546 339668 632480 781025 482175 005354 109446 538358 057434 205185 > 25⁵¹ [i]