MinT - Best Known (57−40, 57, s)-Nets in Base 25

Best Known (57−40, 57, s)-Nets in Base 25

(57−40, 57, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 57, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 57, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]

(57−40, 57, 150)-Net over F₂₅ — Digital

Digital (17, 57, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 57, 150)-net over F₂₅, using
- net from sequence [i] based on digital (16, 149)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 16 and N(F) ≥ 150, using
    - an algebraic function field by Teo [i]

(57−40, 57, 3325)-Net in Base 25 — Upper bound on s

There is no (17, 57, 3326)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 48 246910 953696 293377 152236 550450 739760 376989 892971 992994 708206 383535 928152 803265 > 25⁵⁷ [i]