MinT - Best Known (17, 17+28, s)-Nets in Base 25

Best Known (17, 17+28, s)-Nets in Base 25

(17, 17+28, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 45, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 45, 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]

(17, 17+28, 150)-Net over F₂₅ — Digital

Digital (17, 45, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 45, 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]

(17, 17+28, 7838)-Net in Base 25 — Upper bound on s

There is no (17, 45, 7839)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 808 516095 535799 402431 447147 714084 138841 138634 553956 058739 995825 > 25⁴⁵ [i]