MinT - Best Known (71−50, 71, s)-Nets in Base 25

Best Known (71−50, 71, s)-Nets in Base 25

(71−50, 71, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 71, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 71, 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]

(71−50, 71, 171)-Net over F₂₅ — Digital

Digital (21, 71, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 71, 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]

(71−50, 71, 3945)-Net in Base 25 — Upper bound on s

There is no (21, 71, 3946)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1796 222635 852008 087039 309473 679805 012875 220558 187025 067156 646925 724106 605251 126751 368423 401177 396593 > 25⁷¹ [i]