MinT - Best Known (20, 20+79, s)-Nets in Base 25

Best Known (20, 20+79, s)-Nets in Base 25

(20, 20+79, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 99, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 99, 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+79, 171)-Net over F₂₅ — Digital

Digital (20, 99, 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+79, 2068)-Net in Base 25 — Upper bound on s

There is no (20, 99, 2069)-net in base 25, because

1 times m-reduction [i] would yield (20, 98, 2069)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 100218 886650 460089 628229 571387 887297 755622 124950 190569 948553 587161 289698 679404 052984 922230 995447 892390 913488 676930 821062 432416 445450 842505 > 25⁹⁸ [i]