MinT - Best Known (93−71, 93, s)-Nets in Base 25

Best Known (93−71, 93, s)-Nets in Base 25

(93−71, 93, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 93, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 93, 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]

(93−71, 93, 171)-Net over F₂₅ — Digital

Digital (22, 93, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 93, 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]

(93−71, 93, 2720)-Net in Base 25 — Upper bound on s

There is no (22, 93, 2721)-net in base 25, because

1 times m-reduction [i] would yield (22, 92, 2721)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 408 573227 333763 992581 909577 959542 317417 737890 212275 249473 503722 921724 017488 627830 691900 360119 792515 736012 677496 000309 336236 680457 > 25⁹² [i]