MinT - Best Known (116−69, 116, s)-Nets in Base 3

Best Known (116−69, 116, s)-Nets in Base 3

(116−69, 116, 48)-Net over F₃ — Constructive and digital

Digital (47, 116, 48)-net over F₃, using

t-expansion [i] based on digital (45, 116, 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]

(116−69, 116, 56)-Net over F₃ — Digital

Digital (47, 116, 56)-net over F₃, using

t-expansion [i] based on digital (40, 116, 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]

(116−69, 116, 246)-Net in Base 3 — Upper bound on s

There is no (47, 116, 247)-net in base 3, because

1 times m-reduction [i] would yield (47, 115, 247)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 152575 019572 401891 912559 754281 357279 183761 042865 265197 > 3¹¹⁵ [i]