MinT - Best Known (84−45, 84, s)-Nets in Base 25

Best Known (84−45, 84, s)-Nets in Base 25

(84−45, 84, 208)-Net over F₂₅ — Constructive and digital

Digital (39, 84, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 84, 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]

(84−45, 84, 334)-Net over F₂₅ — Digital

Digital (39, 84, 334)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−45, 84, 70895)-Net in Base 25 — Upper bound on s

There is no (39, 84, 70896)-net in base 25, because

1 times m-reduction [i] would yield (39, 83, 70896)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 106 929431 808730 025332 092846 204247 643370 008679 533172 379066 724329 334840 207543 869543 717533 179530 450678 937197 591379 898625 > 25⁸³ [i]