MinT - Best Known (90−68, 90, s)-Nets in Base 25

Best Known (90−68, 90, s)-Nets in Base 25

(90−68, 90, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 90, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 90, 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]

(90−68, 90, 171)-Net over F₂₅ — Digital

Digital (22, 90, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 90, 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]

(90−68, 90, 2811)-Net in Base 25 — Upper bound on s

There is no (22, 90, 2812)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 656429 608627 936291 189197 155621 853644 859359 867702 309344 324578 003604 386543 476696 456727 509411 735464 920602 554122 746016 997000 968385 > 25⁹⁰ [i]