MinT - Best Known (182, 182+60, s)-Nets in Base 3

Best Known (182, 182+60, s)-Nets in Base 3

(182, 182+60, 328)-Net over F₃ — Constructive and digital

Digital (182, 242, 328)-net over F₃, using

3² times duplication [i] based on digital (180, 240, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 60, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(182, 182+60, 1028)-Net over F₃ — Digital

Digital (182, 242, 1028)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182, 182+60, 42484)-Net in Base 3 — Upper bound on s

There is no (182, 242, 42485)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 063602 792605 796177 927108 820820 913986 157192 792690 043503 569693 273060 451377 839625 853633 698776 351373 563017 174852 671745 > 3²⁴² [i]