MinT - Best Known (21, 21+76, s)-Nets in Base 25

Best Known (21, 21+76, s)-Nets in Base 25

(21, 21+76, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 97, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 97, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(21, 21+76, 171)-Net over F₂₅ — Digital

Digital (21, 97, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 97, 171)-net over F₂₅, using
- net from sequence [i] based on digital (20, 170)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 20 and N(F) ≥ 171, using
    - an algebraic function field by Teo [i]

(21, 21+76, 2297)-Net in Base 25 — Upper bound on s

There is no (21, 97, 2298)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4019 134622 936939 852547 330455 118885 968086 934809 377744 536049 729480 410967 658043 517921 228269 989349 871829 230172 415051 791720 921485 441139 947745 > 25⁹⁷ [i]