MinT - Best Known (15, 15+26, s)-Nets in Base 25

Best Known (15, 15+26, s)-Nets in Base 25

(15, 15+26, 126)-Net over F₂₅ — Constructive and digital

Digital (15, 41, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 41, 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+26, 140)-Net over F₂₅ — Digital

Digital (15, 41, 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+26, 6048)-Net in Base 25 — Upper bound on s

There is no (15, 41, 6049)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2072 302662 290155 615233 720508 523121 727135 594335 638893 823929 > 25⁴¹ [i]