MinT - Best Known (84−64, 84, s)-Nets in Base 25

Best Known (84−64, 84, s)-Nets in Base 25

(84−64, 84, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 84, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 84, 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]

(84−64, 84, 171)-Net over F₂₅ — Digital

Digital (20, 84, 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]

(84−64, 84, 2473)-Net in Base 25 — Upper bound on s

There is no (20, 84, 2474)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2688 276282 324681 898097 404161 222331 030294 574763 817211 379653 314424 947644 447413 185427 285960 556239 909453 456790 039509 598721 > 25⁸⁴ [i]