MinT - Best Known (36−27, 36, s)-Nets in Base 25

Best Known (36−27, 36, s)-Nets in Base 25

(36−27, 36, 104)-Net over F₂₅ — Constructive and digital

Digital (9, 36, 104)-net over F₂₅, using

net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
  - a function field by GarcÃa and Quoos [i]

(36−27, 36, 1363)-Net in Base 25 — Upper bound on s

There is no (9, 36, 1364)-net in base 25, because

1 times m-reduction [i] would yield (9, 35, 1364)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 8 472933 599156 150149 491470 117769 880931 305441 903969 > 25³⁵ [i]