MinT - Best Known (77−34, 77, s)-Nets in Base 25

Best Known (77−34, 77, s)-Nets in Base 25

(77−34, 77, 288)-Net over F₂₅ — Constructive and digital

Digital (43, 77, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 77, 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]

(77−34, 77, 1019)-Net over F₂₅ — Digital

Digital (43, 77, 1019)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−34, 77, 642057)-Net in Base 25 — Upper bound on s

There is no (43, 77, 642058)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 437910 317290 582516 989414 513541 721513 636630 153186 401923 180414 572738 132213 755905 371762 090471 721790 489750 105585 > 25⁷⁷ [i]