MinT - Best Known (20, 20+90, s)-Nets in Base 25

Best Known (20, 20+90, s)-Nets in Base 25

(20, 20+90, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 110, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 110, 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+90, 171)-Net over F₂₅ — Digital

Digital (20, 110, 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+90, 1895)-Net in Base 25 — Upper bound on s

There is no (20, 110, 1896)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 6002 106995 936735 980161 977943 010697 171536 795589 524834 313650 425437 525581 813289 262421 741754 946296 436096 244969 073198 466910 506223 092119 455892 859873 452846 687425 > 25¹¹⁰ [i]