MinT - Best Known (168−72, 168, s)-Nets in Base 3

Best Known (168−72, 168, s)-Nets in Base 3

(168−72, 168, 80)-Net over F₃ — Constructive and digital

Digital (96, 168, 80)-net over F₃, using

8 times m-reduction [i] based on digital (96, 176, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 88, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(168−72, 168, 133)-Net over F₃ — Digital

Digital (96, 168, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(168−72, 168, 1167)-Net in Base 3 — Upper bound on s

There is no (96, 168, 1168)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 143 552829 074489 145950 562972 985037 154242 872643 096484 380634 846002 551597 639169 393025 > 3¹⁶⁸ [i]