MinT - Best Known (168, 168+71, s)-Nets in Base 3

Best Known (168, 168+71, s)-Nets in Base 3

(168, 168+71, 252)-Net over F₃ — Constructive and digital

Digital (168, 239, 252)-net over F₃, using

1 times m-reduction [i] based on digital (168, 240, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 80, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(168, 168+71, 534)-Net over F₃ — Digital

Digital (168, 239, 534)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168, 168+71, 12173)-Net in Base 3 — Upper bound on s

There is no (168, 239, 12174)-net in base 3, because

1 times m-reduction [i] would yield (168, 238, 12174)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 358878 411699 422552 528375 360510 237126 666766 229001 273453 634166 471356 588669 600325 065306 345480 980339 630868 363350 451585 > 3²³⁸ [i]