MinT - Best Known (39, 39+53, s)-Nets in Base 25

Best Known (39, 39+53, s)-Nets in Base 25

(39, 39+53, 208)-Net over F₂₅ — Constructive and digital

Digital (39, 92, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 92, 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]

(39, 39+53, 240)-Net over F₂₅ — Digital

Digital (39, 92, 240)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+53, 34332)-Net in Base 25 — Upper bound on s

There is no (39, 92, 34333)-net in base 25, because

1 times m-reduction [i] would yield (39, 91, 34333)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 16 324689 697352 335213 990968 410241 459266 715207 598155 403810 095015 403195 700192 577839 493738 651164 340444 846336 870287 175044 792419 632241 > 25⁹¹ [i]