MinT - Best Known (40−19, 40, s)-Nets in Base 3

Best Known (40−19, 40, s)-Nets in Base 3

(40−19, 40, 32)-Net over F₃ — Constructive and digital

Digital (21, 40, 32)-net over F₃, using

net from sequence [i] based on digital (21, 31)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(40−19, 40, 35)-Net over F₃ — Digital

Digital (21, 40, 35)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(40−19, 40, 233)-Net in Base 3 — Upper bound on s

There is no (21, 40, 234)-net in base 3, because

1 times m-reduction [i] would yield (21, 39, 234)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 073132 680544 256005 > 3³⁹ [i]