MinT - Best Known (45−24, 45, s)-Nets in Base 25

Best Known (45−24, 45, s)-Nets in Base 25

(45−24, 45, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 45, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 45, 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]

(45−24, 45, 225)-Net over F₂₅ — Digital

Digital (21, 45, 225)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(45−24, 45, 38490)-Net in Base 25 — Upper bound on s

There is no (21, 45, 38491)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 807 831065 553110 795211 184612 511698 376156 484008 955381 795169 598305 > 25⁴⁵ [i]