MinT - Best Known (51−31, 51, s)-Nets in Base 25

Best Known (51−31, 51, s)-Nets in Base 25

(51−31, 51, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 51, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 51, 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]

(51−31, 51, 171)-Net over F₂₅ — Digital

Digital (20, 51, 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]

(51−31, 51, 12220)-Net in Base 25 — Upper bound on s

There is no (20, 51, 12221)-net in base 25, because

1 times m-reduction [i] would yield (20, 50, 12221)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 7894 648857 987703 283428 631650 282749 255199 285909 345494 199350 764081 337481 > 25⁵⁰ [i]