MinT - Best Known (209−52, 209, s)-Nets in Base 3

Best Known (209−52, 209, s)-Nets in Base 3

(209−52, 209, 328)-Net over F₃ — Constructive and digital

Digital (157, 209, 328)-net over F₃, using

3¹ times duplication [i] based on digital (156, 208, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 52, 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]

(209−52, 209, 898)-Net over F₃ — Digital

Digital (157, 209, 898)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−52, 209, 36080)-Net in Base 3 — Upper bound on s

There is no (157, 209, 36081)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5228 519076 041638 763930 915650 403599 288660 294437 953266 289103 086006 162886 837056 324973 928306 383095 135817 > 3²⁰⁹ [i]