MinT - Best Known (21, 21+65, s)-Nets in Base 25

Best Known (21, 21+65, s)-Nets in Base 25

(21, 21+65, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 86, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 86, 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+65, 171)-Net over F₂₅ — Digital

Digital (21, 86, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 86, 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+65, 2737)-Net in Base 25 — Upper bound on s

There is no (21, 86, 2738)-net in base 25, because

1 times m-reduction [i] would yield (21, 85, 2738)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 67533 801780 573433 627485 588653 464053 267304 977977 556551 682874 910241 920043 172361 657855 193493 484523 371265 722842 556573 010433 > 25⁸⁵ [i]