MinT - Best Known (23, 23+83, s)-Nets in Base 25

Best Known (23, 23+83, s)-Nets in Base 25

(23, 23+83, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 106, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 106, 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]

(23, 23+83, 176)-Net over F₂₅ — Digital

Digital (23, 106, 176)-net over F₂₅, using

net from sequence [i] based on digital (23, 175)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 23 and N(F) ≥ 176, using
  - an algebraic function field by Teo [i]

(23, 23+83, 2535)-Net in Base 25 — Upper bound on s

There is no (23, 106, 2536)-net in base 25, because

1 times m-reduction [i] would yield (23, 105, 2536)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 610 712575 145079 912813 727773 624662 147047 613157 868503 430200 303794 999146 403076 912455 944049 383988 296861 218541 648425 172054 913431 769430 137314 497190 770625 > 25¹⁰⁵ [i]