MinT - Best Known (211−51, 211, s)-Nets in Base 3

Best Known (211−51, 211, s)-Nets in Base 3

(211−51, 211, 400)-Net over F₃ — Constructive and digital

Digital (160, 211, 400)-net over F₃, using

1 times m-reduction [i] based on digital (160, 212, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 53, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(211−51, 211, 1017)-Net over F₃ — Digital

Digital (160, 211, 1017)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−51, 211, 51785)-Net in Base 3 — Upper bound on s

There is no (160, 211, 51786)-net in base 3, because

1 times m-reduction [i] would yield (160, 210, 51786)-net in base 3, but
- 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]