MinT - Best Known (81−54, 81, s)-Nets in Base 25

Best Known (81−54, 81, s)-Nets in Base 25

(81−54, 81, 200)-Net over F₂₅ — Constructive and digital

Digital (27, 81, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 81, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(81−54, 81, 7098)-Net in Base 25 — Upper bound on s

There is no (27, 81, 7099)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 171530 786025 268787 627648 564681 354439 585488 490246 223741 303296 995232 330011 234552 240861 653887 924100 442649 967437 264601 > 25⁸¹ [i]