MinT - Best Known (160−47, 160, s)-Nets in Base 3

Best Known (160−47, 160, s)-Nets in Base 3

(160−47, 160, 228)-Net over F₃ — Constructive and digital

Digital (113, 160, 228)-net over F₃, using

3¹ times duplication [i] based on digital (112, 159, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 53, 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]

(160−47, 160, 393)-Net over F₃ — Digital

Digital (113, 160, 393)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−47, 160, 9348)-Net in Base 3 — Upper bound on s

There is no (113, 160, 9349)-net in base 3, because

1 times m-reduction [i] would yield (113, 159, 9349)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7290 896606 776602 688193 883577 520812 435205 495499 219209 595462 885424 986554 492955 > 3¹⁵⁹ [i]