MinT - Best Known (107−60, 107, s)-Nets in Base 3

Best Known (107−60, 107, s)-Nets in Base 3

(107−60, 107, 48)-Net over F₃ — Constructive and digital

Digital (47, 107, 48)-net over F₃, using

t-expansion [i] based on digital (45, 107, 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]

(107−60, 107, 56)-Net over F₃ — Digital

Digital (47, 107, 56)-net over F₃, using

t-expansion [i] based on digital (40, 107, 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]

(107−60, 107, 274)-Net in Base 3 — Upper bound on s

There is no (47, 107, 275)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1164 286146 755067 000648 357331 541051 642012 393797 416013 > 3¹⁰⁷ [i]