MinT - Best Known (31−27, 31, s)-Nets in Base 25

Best Known (31−27, 31, s)-Nets in Base 25

(31−27, 31, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 31, 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]

(31−27, 31, 390)-Net in Base 25 — Upper bound on s

There is no (4, 31, 391)-net in base 25, because

1 times m-reduction [i] would yield (4, 30, 391)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 871104 934506 644575 896464 752182 573362 667145 > 25³⁰ [i]