MinT - Best Known (8, 32, s)-Nets in Base 25

Best Known (8, 32, s)-Nets in Base 25

(8, 32, 66)-Net over F₂₅ — Constructive and digital

Digital (8, 32, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 32, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(8, 32, 84)-Net over F₂₅ — Digital

Digital (8, 32, 84)-net over F₂₅, using

net from sequence [i] based on digital (8, 83)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 8 and N(F) ≥ 84, using
  - an algebraic function field by Teo [i]

(8, 32, 1171)-Net in Base 25 — Upper bound on s

There is no (8, 32, 1172)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 544 387719 132190 554312 135621 148185 042816 223105 > 25³² [i]