MinT - Best Known (82−58, 82, s)-Nets in Base 25

Best Known (82−58, 82, s)-Nets in Base 25

(82−58, 82, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 82, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 82, 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]

(82−58, 82, 184)-Net over F₂₅ — Digital

Digital (24, 82, 184)-net over F₂₅, using

net from sequence [i] based on digital (24, 183)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 24 and N(F) ≥ 184, using
  - an algebraic function field by Teo [i]

(82−58, 82, 4347)-Net in Base 25 — Upper bound on s

There is no (24, 82, 4348)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 304522 226476 896867 266560 588721 895195 136382 383021 950565 015057 770321 886806 516626 756440 435158 115072 986107 780794 332705 > 25⁸² [i]