MinT - Best Known (15, 15+32, s)-Nets in Base 25

Best Known (15, 15+32, s)-Nets in Base 25

(15, 15+32, 126)-Net over F₂₅ — Constructive and digital

Digital (15, 47, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 47, 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]

(15, 15+32, 140)-Net over F₂₅ — Digital

Digital (15, 47, 140)-net over F₂₅, using

net from sequence [i] based on digital (15, 139)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 15 and N(F) ≥ 140, using
  - an algebraic function field by Teo [i]

(15, 15+32, 3612)-Net in Base 25 — Upper bound on s

There is no (15, 47, 3613)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 506206 958379 650647 978399 409941 100774 859533 937546 082891 394072 171905 > 25⁴⁷ [i]