MinT - Best Known (86−64, 86, s)-Nets in Base 25

Best Known (86−64, 86, s)-Nets in Base 25

(86−64, 86, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 86, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 86, 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]

(86−64, 86, 171)-Net over F₂₅ — Digital

Digital (22, 86, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 86, 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]

(86−64, 86, 3028)-Net in Base 25 — Upper bound on s

There is no (22, 86, 3029)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 679145 483266 221384 317783 553242 942659 595508 945582 919660 192912 779864 110037 125412 049613 374728 493212 481994 237149 464208 327425 > 25⁸⁶ [i]