MinT - Best Known (15, 15+74, s)-Nets in Base 25

Best Known (15, 15+74, s)-Nets in Base 25

(15, 15+74, 126)-Net over F₂₅ — Constructive and digital

Digital (15, 89, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 89, 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+74, 140)-Net over F₂₅ — Digital

Digital (15, 89, 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+74, 1387)-Net in Base 25 — Upper bound on s

There is no (15, 89, 1388)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 26390 702546 825491 350633 536319 082051 986257 005742 275591 020568 642251 464542 129318 934992 536780 953035 251365 810931 593625 008547 248545 > 25⁸⁹ [i]