MinT - Best Known (21−13, 21, s)-Nets in Base 25

Best Known (21−13, 21, s)-Nets in Base 25

(21−13, 21, 66)-Net over F₂₅ — Constructive and digital

Digital (8, 21, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 21, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(21−13, 21, 84)-Net over F₂₅ — Digital

Digital (8, 21, 84)-net over F₂₅, using

net from sequence [i] based on digital (8, 83)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 8 and N(F) ≥ 84, using
  - an algebraic function field by Teo [i]

(21−13, 21, 5696)-Net in Base 25 — Upper bound on s

There is no (8, 21, 5697)-net in base 25, because

1 times m-reduction [i] would yield (8, 20, 5697)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 9100 591659 726244 416700 692049 > 25²⁰ [i]