MinT - Best Known (66−39, 66, s)-Nets in Base 25

Best Known (66−39, 66, s)-Nets in Base 25

(66−39, 66, 200)-Net over F₂₅ — Constructive and digital

Digital (27, 66, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 66, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(66−39, 66, 20008)-Net in Base 25 — Upper bound on s

There is no (27, 66, 20009)-net in base 25, because

1 times m-reduction [i] would yield (27, 65, 20009)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 7 349162 469647 006359 694225 976157 584545 135934 509934 270562 260377 636152 714967 041417 159146 855625 > 25⁶⁵ [i]