MinT - Best Known (119−73, 119, s)-Nets in Base 3

Best Known (119−73, 119, s)-Nets in Base 3

(119−73, 119, 48)-Net over F₃ — Constructive and digital

Digital (46, 119, 48)-net over F₃, using

t-expansion [i] based on digital (45, 119, 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]

(119−73, 119, 56)-Net over F₃ — Digital

Digital (46, 119, 56)-net over F₃, using

t-expansion [i] based on digital (40, 119, 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]

(119−73, 119, 227)-Net in Base 3 — Upper bound on s

There is no (46, 119, 228)-net in base 3, because

1 times m-reduction [i] would yield (46, 118, 228)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 200 942838 279407 756954 793509 800257 385461 404561 500252 829633 > 3¹¹⁸ [i]