MinT - Best Known (101−80, 101, s)-Nets in Base 25

Best Known (101−80, 101, s)-Nets in Base 25

(101−80, 101, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 101, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 101, 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]

(101−80, 101, 171)-Net over F₂₅ — Digital

Digital (21, 101, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 101, 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]

(101−80, 101, 2204)-Net in Base 25 — Upper bound on s

There is no (21, 101, 2205)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1580 374908 143410 589952 101985 512700 341890 626964 547130 552223 298173 781534 133085 135482 682730 084009 358988 446846 283626 510908 583548 056677 297196 277185 > 25¹⁰¹ [i]