MinT - Best Known (208−56, 208, s)-Nets in Base 3

Best Known (208−56, 208, s)-Nets in Base 3

(208−56, 208, 288)-Net over F₃ — Constructive and digital

Digital (152, 208, 288)-net over F₃, using

t-expansion [i] based on digital (151, 208, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (151, 210, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 70, 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]

(208−56, 208, 663)-Net over F₃ — Digital

Digital (152, 208, 663)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−56, 208, 19756)-Net in Base 3 — Upper bound on s

There is no (152, 208, 19757)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1744 984036 701793 497175 416014 543894 473518 857616 872071 903358 130186 767112 685406 360758 651704 048723 299633 > 3²⁰⁸ [i]