MinT - Best Known (164−72, 164, s)-Nets in Base 3

Best Known (164−72, 164, s)-Nets in Base 3

(164−72, 164, 80)-Net over F₃ — Constructive and digital

Digital (92, 164, 80)-net over F₃, using

4 times m-reduction [i] based on digital (92, 168, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 84, 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]

(164−72, 164, 122)-Net over F₃ — Digital

Digital (92, 164, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−72, 164, 1029)-Net in Base 3 — Upper bound on s

There is no (92, 164, 1030)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 783808 426470 498223 378408 009973 256144 632668 909830 987671 032931 018956 900746 975305 > 3¹⁶⁴ [i]