MinT - Best Known (99−77, 99, s)-Nets in Base 25

Best Known (99−77, 99, s)-Nets in Base 25

(99−77, 99, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 99, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 99, 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]

(99−77, 99, 171)-Net over F₂₅ — Digital

Digital (22, 99, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 99, 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]

(99−77, 99, 2502)-Net in Base 25 — Upper bound on s

There is no (22, 99, 2503)-net in base 25, because

1 times m-reduction [i] would yield (22, 98, 2503)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 100617 320541 398095 686145 733480 915493 808497 086608 296639 558663 367699 482332 604423 984214 055054 996893 351239 052503 707878 751255 853300 486554 160625 > 25⁹⁸ [i]