MinT - Best Known (21, 89, s)-Nets in Base 25

Best Known (21, 89, s)-Nets in Base 25

(21, 89, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 89, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 89, 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]

(21, 89, 171)-Net over F₂₅ — Digital

Digital (21, 89, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 89, 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]

(21, 89, 2555)-Net in Base 25 — Upper bound on s

There is no (21, 89, 2556)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 26125 746706 452063 539067 426678 182464 772586 685457 356278 955706 095079 995567 378026 685866 919901 457715 194890 903258 847616 582088 927425 > 25⁸⁹ [i]