MinT - Best Known (21, 21+82, s)-Nets in Base 25

Best Known (21, 21+82, s)-Nets in Base 25

(21, 21+82, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 103, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 103, 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]

(21, 21+82, 171)-Net over F₂₅ — Digital

Digital (21, 103, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 103, 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]

(21, 21+82, 2164)-Net in Base 25 — Upper bound on s

There is no (21, 103, 2165)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 989156 208589 764860 970603 388080 964983 194443 404236 971432 382990 881364 065719 304623 864026 762594 742043 522582 472875 829532 628403 035899 454393 949069 143225 > 25¹⁰³ [i]