MinT - Best Known (70−48, 70, s)-Nets in Base 25

Best Known (70−48, 70, s)-Nets in Base 25

(70−48, 70, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 70, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 70, 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]

(70−48, 70, 171)-Net over F₂₅ — Digital

Digital (22, 70, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 70, 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]

(70−48, 70, 4868)-Net in Base 25 — Upper bound on s

There is no (22, 70, 4869)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 72 048918 719330 654350 963508 991647 374938 077634 974949 303625 789493 966696 527136 880202 446795 684015 849025 > 25⁷⁰ [i]