MinT - Best Known (37, 37+57, s)-Nets in Base 25

Best Known (37, 37+57, s)-Nets in Base 25

(37, 37+57, 208)-Net over F₂₅ — Constructive and digital

Digital (37, 94, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 94, 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]

(37, 37+57, 20684)-Net in Base 25 — Upper bound on s

There is no (37, 94, 20685)-net in base 25, because

1 times m-reduction [i] would yield (37, 93, 20685)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 10203 435145 115085 083205 698910 878284 745994 360099 689640 385750 436439 748719 050266 754721 618218 224244 354141 651847 980812 622518 241828 156833 > 25⁹³ [i]