MinT - Best Known (218−58, 218, s)-Nets in Base 3

Best Known (218−58, 218, s)-Nets in Base 3

(218−58, 218, 288)-Net over F₃ — Constructive and digital

Digital (160, 218, 288)-net over F₃, using

t-expansion [i] based on digital (159, 218, 288)-net over F₃, using
- 4 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]

(218−58, 218, 720)-Net over F₃ — Digital

Digital (160, 218, 720)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−58, 218, 22499)-Net in Base 3 — Upper bound on s

There is no (160, 218, 22500)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 102 933952 523685 278790 154881 451507 397473 264424 317375 827067 676061 004503 604161 282864 891167 127139 156961 173801 > 3²¹⁸ [i]