MinT - Best Known (212−62, 212, s)-Nets in Base 3

Best Known (212−62, 212, s)-Nets in Base 3

(212−62, 212, 252)-Net over F₃ — Constructive and digital

Digital (150, 212, 252)-net over F₃, using

1 times m-reduction [i] based on digital (150, 213, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 71, 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]

(212−62, 212, 506)-Net over F₃ — Digital

Digital (150, 212, 506)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−62, 212, 11343)-Net in Base 3 — Upper bound on s

There is no (150, 212, 11344)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141504 245937 790266 127133 269335 700869 448731 649991 439795 520678 822280 825179 128629 511882 730481 027059 233729 > 3²¹² [i]