MinT - Best Known (15, 15+76, s)-Nets in Base 25

Best Known (15, 15+76, s)-Nets in Base 25

(15, 15+76, 126)-Net over F₂₅ — Constructive and digital

Digital (15, 91, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 91, 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+76, 140)-Net over F₂₅ — Digital

Digital (15, 91, 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+76, 1374)-Net in Base 25 — Upper bound on s

There is no (15, 91, 1375)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 16 731936 271327 829215 126633 143542 189186 722496 852916 695570 360593 822931 583660 839816 390098 867333 460691 471002 109014 729680 043424 132721 > 25⁹¹ [i]