MinT - Best Known (210−50, 210, s)-Nets in Base 3

Best Known (210−50, 210, s)-Nets in Base 3

(210−50, 210, 464)-Net over F₃ — Constructive and digital

Digital (160, 210, 464)-net over F₃, using

3² times duplication [i] based on digital (158, 208, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 52, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(210−50, 210, 1078)-Net over F₃ — Digital

Digital (160, 210, 1078)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−50, 210, 51785)-Net in Base 3 — Upper bound on s

There is no (160, 210, 51786)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15687 284940 183981 001171 079158 044267 093011 933127 043759 856619 239730 494306 390147 881384 114938 928550 208805 > 3²¹⁰ [i]