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

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

(31−25, 31, 66)-Net over F₂₅ — Constructive and digital

Digital (6, 31, 66)-net over F₂₅, using

t-expansion [i] based on 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]

(31−25, 31, 682)-Net in Base 25 — Upper bound on s

There is no (6, 31, 683)-net in base 25, because

1 times m-reduction [i] would yield (6, 30, 683)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 872432 632107 903017 198893 839827 962147 684705 > 25³⁰ [i]