MinT - Best Known (20, 20+80, s)-Nets in Base 25

Best Known (20, 20+80, s)-Nets in Base 25

(20, 20+80, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 100, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 100, 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]

(20, 20+80, 171)-Net over F₂₅ — Digital

Digital (20, 100, 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]

(20, 20+80, 2032)-Net in Base 25 — Upper bound on s

There is no (20, 100, 2033)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 63 360551 006930 083136 013186 718656 205721 575589 074411 535809 020598 343862 173423 154742 789762 450810 975556 126673 324323 677024 068559 389016 691341 036225 > 25¹⁰⁰ [i]