MinT - Best Known (22, 109, s)-Nets in Base 25

Best Known (22, 109, s)-Nets in Base 25

(22, 109, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 109, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 109, 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]

(22, 109, 171)-Net over F₂₅ — Digital

Digital (22, 109, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 109, 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]

(22, 109, 2259)-Net in Base 25 — Upper bound on s

There is no (22, 109, 2260)-net in base 25, because

1 times m-reduction [i] would yield (22, 108, 2260)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 9 584538 310693 203488 604365 259041 584414 900815 642488 051692 896119 511904 037305 311573 805318 797464 661475 152098 167436 012368 948472 021143 386940 670942 358235 873825 > 25¹⁰⁸ [i]