MinT - Best Known (51−28, 51, s)-Nets in Base 25

Best Known (51−28, 51, s)-Nets in Base 25

(51−28, 51, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 51, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 51, 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]

(51−28, 51, 204)-Net over F₂₅ — Digital

Digital (23, 51, 204)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(51−28, 51, 31163)-Net in Base 25 — Upper bound on s

There is no (23, 51, 31164)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 197276 567621 195494 097513 518689 500051 281089 607391 930123 090548 137666 210625 > 25⁵¹ [i]