MinT - Best Known (95−73, 95, s)-Nets in Base 25

Best Known (95−73, 95, s)-Nets in Base 25

(95−73, 95, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 95, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 95, 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]

(95−73, 95, 171)-Net over F₂₅ — Digital

Digital (22, 95, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 95, 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]

(95−73, 95, 2639)-Net in Base 25 — Upper bound on s

There is no (22, 95, 2640)-net in base 25, because

1 times m-reduction [i] would yield (22, 94, 2640)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 255123 336757 684657 880322 018234 796378 465493 192500 186059 751825 017241 354360 525205 171484 885647 124102 690719 509255 792327 225299 234930 706945 > 25⁹⁴ [i]