MinT - Best Known (215−47, 215, s)-Nets in Base 3

Best Known (215−47, 215, s)-Nets in Base 3

(215−47, 215, 640)-Net over F₃ — Constructive and digital

Digital (168, 215, 640)-net over F₃, using

t-expansion [i] based on digital (167, 215, 640)-net over F₃, using
- 1 times m-reduction [i] based on digital (167, 216, 640)-net over F₃, using
  - trace code for nets [i] based on digital (5, 54, 160)-net over F₈₁, using
    - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
        a function field by SÃ©mirat [i]

(215−47, 215, 1551)-Net over F₃ — Digital

Digital (168, 215, 1551)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−47, 215, 129614)-Net in Base 3 — Upper bound on s

There is no (168, 215, 129615)-net in base 3, because

1 times m-reduction [i] would yield (168, 214, 129615)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 270574 787427 917869 635566 581285 818760 761024 929007 657799 105702 951474 320205 664201 330958 807931 749391 459859 > 3²¹⁴ [i]