MinT - Best Known (45, 45+57, s)-Nets in Base 3

Best Known (45, 45+57, s)-Nets in Base 3

(45, 45+57, 48)-Net over F₃ — Constructive and digital

Digital (45, 102, 48)-net over F₃, using

net from sequence [i] based on digital (45, 47)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
  - an explicitly constructive algebraic function field [i]

(45, 45+57, 56)-Net over F₃ — Digital

Digital (45, 102, 56)-net over F₃, using

t-expansion [i] based on digital (40, 102, 56)-net over F₃, using
- net from sequence [i] based on digital (40, 55)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
    - a curve from the manYPoints database [i]

(45, 45+57, 270)-Net in Base 3 — Upper bound on s

There is no (45, 102, 271)-net in base 3, because

1 times m-reduction [i] would yield (45, 101, 271)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 591696 149125 503805 620686 835317 128536 636149 811401 > 3¹⁰¹ [i]