MinT - Best Known (21, 21+89, s)-Nets in Base 25

Best Known (21, 21+89, s)-Nets in Base 25

(21, 21+89, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 110, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 110, 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+89, 171)-Net over F₂₅ — Digital

Digital (21, 110, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 110, 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+89, 2065)-Net in Base 25 — Upper bound on s

There is no (21, 110, 2066)-net in base 25, because

1 times m-reduction [i] would yield (21, 109, 2066)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 242 384110 658501 771440 922072 061249 552966 698948 457203 414019 295249 366549 082828 291576 441964 735937 027200 805418 778108 302512 871260 943723 290662 322666 099185 983425 > 25¹⁰⁹ [i]