MinT - Best Known (212−63, 212, s)-Nets in Base 3

Best Known (212−63, 212, s)-Nets in Base 3

(212−63, 212, 246)-Net over F₃ — Constructive and digital

Digital (149, 212, 246)-net over F₃, using

1 times m-reduction [i] based on digital (149, 213, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 71, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(212−63, 212, 480)-Net over F₃ — Digital

Digital (149, 212, 480)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−63, 212, 10947)-Net in Base 3 — Upper bound on s

There is no (149, 212, 10948)-net in base 3, because

1 times m-reduction [i] would yield (149, 211, 10948)-net in base 3, but
- 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]