MinT - Best Known (27, 27+16, s)-Nets in Base 3

Best Known (27, 27+16, s)-Nets in Base 3

(27, 27+16, 64)-Net over F₃ — Constructive and digital

Digital (27, 43, 64)-net over F₃, using

1 times m-reduction [i] based on digital (27, 44, 64)-net over F₃, using
- trace code for nets [i] based on digital (5, 22, 32)-net over F₉, using
  - net from sequence [i] based on digital (5, 31)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]

(27, 27+16, 72)-Net over F₃ — Digital

Digital (27, 43, 72)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(27, 27+16, 683)-Net in Base 3 — Upper bound on s

There is no (27, 43, 684)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 331 807442 487386 756545 > 3⁴³ [i]