MinT - Best Known (39, 39+57, s)-Nets in Base 25

Best Known (39, 39+57, s)-Nets in Base 25

(39, 39+57, 208)-Net over F₂₅ — Constructive and digital

Digital (39, 96, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 96, 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+57, 211)-Net over F₂₅ — Digital

Digital (39, 96, 211)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+57, 26035)-Net in Base 25 — Upper bound on s

There is no (39, 96, 26036)-net in base 25, because

1 times m-reduction [i] would yield (39, 95, 26036)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 6 378236 810768 763560 028265 790802 866936 560364 159732 798334 495481 976162 838484 357656 548597 230037 492280 278761 522638 306161 204722 892416 834945 > 25⁹⁵ [i]