MinT - Best Known (65, 65+27, s)-Nets in Base 3

Best Known (65, 65+27, s)-Nets in Base 3

(65, 65+27, 156)-Net over F₃ — Constructive and digital

Digital (65, 92, 156)-net over F₃, using

1 times m-reduction [i] based on digital (65, 93, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 31, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(65, 65+27, 258)-Net over F₃ — Digital

Digital (65, 92, 258)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+27, 6185)-Net in Base 3 — Upper bound on s

There is no (65, 92, 6186)-net in base 3, because

1 times m-reduction [i] would yield (65, 91, 6186)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26 231666 637272 623422 728411 701423 168657 547229 > 3⁹¹ [i]