MinT - Best Known (26−17, 26, s)-Nets in Base 3

Best Known (26−17, 26, s)-Nets in Base 3

(26−17, 26, 19)-Net over F₃ — Constructive and digital

Digital (9, 26, 19)-net over F₃, using

net from sequence [i] based on digital (9, 18)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using
  - an explicitly constructive algebraic function field [i]

(26−17, 26, 51)-Net in Base 3 — Upper bound on s

There is no (9, 26, 52)-net in base 3, because

1 times m-reduction [i] would yield (9, 25, 52)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 947829 851073 > 3²⁵ [i]