MinT - Best Known (164−70, 164, s)-Nets in Base 3

Best Known (164−70, 164, s)-Nets in Base 3

(164−70, 164, 80)-Net over F₃ — Constructive and digital

Digital (94, 164, 80)-net over F₃, using

8 times m-reduction [i] based on digital (94, 172, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 86, 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]

(164−70, 164, 131)-Net over F₃ — Digital

Digital (94, 164, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−70, 164, 1162)-Net in Base 3 — Upper bound on s

There is no (94, 164, 1163)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 804145 585003 106466 412524 454557 174370 928949 376394 958929 598460 648604 603823 366155 > 3¹⁶⁴ [i]