MinT - Best Known (146, 194, s)-Nets in Base 3

Best Known (146, 194, s)-Nets in Base 3

(146, 194, 328)-Net over F₃ — Constructive and digital

Digital (146, 194, 328)-net over F₃, using

3² times duplication [i] based on digital (144, 192, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 48, 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]

(146, 194, 864)-Net over F₃ — Digital

Digital (146, 194, 864)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 194, 35218)-Net in Base 3 — Upper bound on s

There is no (146, 194, 35219)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 429302 866060 093348 350730 588304 945842 567802 865442 866407 923867 901048 439905 966287 837019 117009 > 3¹⁹⁴ [i]