MinT - Best Known (82−44, 82, s)-Nets in Base 25

Best Known (82−44, 82, s)-Nets in Base 25

(82−44, 82, 208)-Net over F₂₅ — Constructive and digital

Digital (38, 82, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 82, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(82−44, 82, 324)-Net over F₂₅ — Digital

Digital (38, 82, 324)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−44, 82, 61244)-Net in Base 25 — Upper bound on s

There is no (38, 82, 61245)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 277751 854152 391943 395858 343175 081846 801512 485091 793223 014384 066102 249806 110763 743090 893021 981589 860367 559881 209105 > 25⁸² [i]