MinT - Best Known (53−31, 53, s)-Nets in Base 25

Best Known (53−31, 53, s)-Nets in Base 25

(53−31, 53, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 53, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 53, 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]

(53−31, 53, 171)-Net over F₂₅ — Digital

Digital (22, 53, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 53, 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]

(53−31, 53, 18774)-Net in Base 25 — Upper bound on s

There is no (22, 53, 18775)-net in base 25, because

1 times m-reduction [i] would yield (22, 52, 18775)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 931886 517109 481757 690156 633457 555325 130687 929795 807511 348598 983754 508121 > 25⁵² [i]