MinT - Best Known (55−34, 55, s)-Nets in Base 25

Best Known (55−34, 55, s)-Nets in Base 25

(55−34, 55, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 55, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 55, 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]

(55−34, 55, 171)-Net over F₂₅ — Digital

Digital (21, 55, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 55, 171)-net over F₂₅, using
- net from sequence [i] based on digital (20, 170)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 20 and N(F) ≥ 171, using
    - an algebraic function field by Teo [i]

(55−34, 55, 9956)-Net in Base 25 — Upper bound on s

There is no (21, 55, 9957)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 77118 788078 099483 784872 272812 441976 469046 593959 178606 734293 050323 351255 538425 > 25⁵⁵ [i]