MinT - Best Known (211−62, 211, s)-Nets in Base 3

Best Known (211−62, 211, s)-Nets in Base 3

(211−62, 211, 252)-Net over F₃ — Constructive and digital

Digital (149, 211, 252)-net over F₃, using

3¹ times duplication [i] based on digital (148, 210, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 70, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(211−62, 211, 496)-Net over F₃ — Digital

Digital (149, 211, 496)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−62, 211, 10947)-Net in Base 3 — Upper bound on s

There is no (149, 211, 10948)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47173 481972 462849 833045 019219 393123 869229 613761 158508 587259 018249 402436 676174 322430 806405 215755 082929 > 3²¹¹ [i]