MinT - Best Known (159, 207, s)-Nets in Base 3

Best Known (159, 207, s)-Nets in Base 3

(159, 207, 464)-Net over F₃ — Constructive and digital

Digital (159, 207, 464)-net over F₃, using

t-expansion [i] based on digital (158, 207, 464)-net over F₃, using
- 1 times m-reduction [i] based on digital (158, 208, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 52, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(159, 207, 1183)-Net over F₃ — Digital

Digital (159, 207, 1183)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 207, 63876)-Net in Base 3 — Upper bound on s

There is no (159, 207, 63877)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 580 919278 739366 257903 536782 035384 362224 173191 247789 253791 770081 532640 247158 368974 105894 411874 162977 > 3²⁰⁷ [i]