MinT - Best Known (55−51, 55, s)-Nets in Base 25

Best Known (55−51, 55, s)-Nets in Base 25

(55−51, 55, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 55, 66)-net over F₂₅, using

net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]

(55−51, 55, 387)-Net in Base 25 — Upper bound on s

There is no (4, 55, 388)-net in base 25, because

19 times m-reduction [i] would yield (4, 36, 388)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 212 867301 584337 671224 184862 902302 351269 285411 623425 > 25³⁶ [i]