MinT - Best Known (57−35, 57, s)-Nets in Base 25

Best Known (57−35, 57, s)-Nets in Base 25

(57−35, 57, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 57, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 57, 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]

(57−35, 57, 171)-Net over F₂₅ — Digital

Digital (22, 57, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 57, 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]

(57−35, 57, 12033)-Net in Base 25 — Upper bound on s

There is no (22, 57, 12034)-net in base 25, because

1 times m-reduction [i] would yield (22, 56, 12034)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 926781 825633 322538 661191 972049 333314 559167 213221 791058 770755 213732 300975 964465 > 25⁵⁶ [i]