MinT - Best Known (85−47, 85, s)-Nets in Base 25

Best Known (85−47, 85, s)-Nets in Base 25

(85−47, 85, 208)-Net over F₂₅ — Constructive and digital

Digital (38, 85, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 85, 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]

(85−47, 85, 281)-Net over F₂₅ — Digital

Digital (38, 85, 281)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−47, 85, 50079)-Net in Base 25 — Upper bound on s

There is no (38, 85, 50080)-net in base 25, because

1 times m-reduction [i] would yield (38, 84, 50080)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2673 180256 463829 670284 793826 530188 803763 205420 390521 031295 691904 626345 043061 767607 904259 195771 429272 174658 697660 945665 > 25⁸⁴ [i]