MinT - Best Known (92−50, 92, s)-Nets in Base 25

Best Known (92−50, 92, s)-Nets in Base 25

(92−50, 92, 288)-Net over F₂₅ — Constructive and digital

Digital (42, 92, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 92, 288)-net over F₂₅, using
- net from sequence [i] based on digital (41, 287)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
    - a function field by GarcÃa and Quoos [i]

(92−50, 92, 330)-Net over F₂₅ — Digital

Digital (42, 92, 330)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−50, 92, 59120)-Net in Base 25 — Upper bound on s

There is no (42, 92, 59121)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 407 919359 644890 309575 396605 484425 869505 825482 099959 949240 311598 714747 713278 739274 536131 624495 120309 204874 990608 965010 886763 980761 > 25⁹² [i]