MinT - Best Known (109−71, 109, s)-Nets in Base 25

Best Known (109−71, 109, s)-Nets in Base 25

(109−71, 109, 208)-Net over F₂₅ — Constructive and digital

Digital (38, 109, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 109, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(109−71, 109, 11913)-Net in Base 25 — Upper bound on s

There is no (38, 109, 11914)-net in base 25, because

1 times m-reduction [i] would yield (38, 108, 11914)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 9 521383 143243 040427 615881 625593 962785 860323 376126 677032 826112 078441 870702 135240 522647 645926 788741 181697 430246 064375 190325 249425 353743 324845 441711 107089 > 25¹⁰⁸ [i]