MinT - Best Known (159, 159+70, s)-Nets in Base 3

Best Known (159, 159+70, s)-Nets in Base 3

(159, 159+70, 228)-Net over F₃ — Constructive and digital

Digital (159, 229, 228)-net over F₃, using

3¹ times duplication [i] based on digital (158, 228, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 76, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(159, 159+70, 470)-Net over F₃ — Digital

Digital (159, 229, 470)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+70, 9169)-Net in Base 3 — Upper bound on s

There is no (159, 229, 9170)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 269861 249910 624021 378835 184121 732342 273504 998354 302200 476934 162135 042410 571518 844652 106849 734253 850160 189905 > 3²²⁹ [i]