MinT - Best Known (79−32, 79, s)-Nets in Base 25

Best Known (79−32, 79, s)-Nets in Base 25

(79−32, 79, 288)-Net over F₂₅ — Constructive and digital

Digital (47, 79, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 79, 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]

(79−32, 79, 1905)-Net over F₂₅ — Digital

Digital (47, 79, 1905)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−32, 79, 2262844)-Net in Base 25 — Upper bound on s

There is no (47, 79, 2262845)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 273 692098 464701 133135 160885 781259 320661 809826 007553 919913 301000 049589 628559 832917 875049 718497 855218 187743 929729 > 25⁷⁹ [i]