MinT - Best Known (77−57, 77, s)-Nets in Base 25

Best Known (77−57, 77, s)-Nets in Base 25

(77−57, 77, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 77, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 77, 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]

(77−57, 77, 171)-Net over F₂₅ — Digital

Digital (20, 77, 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]

(77−57, 77, 2917)-Net in Base 25 — Upper bound on s

There is no (20, 77, 2918)-net in base 25, because

1 times m-reduction [i] would yield (20, 76, 2918)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 17581 680179 900372 841136 823438 204757 916337 488854 489904 639817 261977 836965 817814 388391 050211 529770 326650 480705 > 25⁷⁶ [i]