MinT - Best Known (216−56, 216, s)-Nets in Base 3

Best Known (216−56, 216, s)-Nets in Base 3

(216−56, 216, 288)-Net over F₃ — Constructive and digital

Digital (160, 216, 288)-net over F₃, using

t-expansion [i] based on digital (159, 216, 288)-net over F₃, using
- 6 times m-reduction [i] based on digital (159, 222, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 74, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(216−56, 216, 787)-Net over F₃ — Digital

Digital (160, 216, 787)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−56, 216, 27051)-Net in Base 3 — Upper bound on s

There is no (160, 216, 27052)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 445420 967226 025207 005144 015343 425445 280986 796763 812030 613535 401727 492640 522724 183965 021343 252008 486977 > 3²¹⁶ [i]