MinT - Best Known (171−40, 171, s)-Nets in Base 3

Best Known (171−40, 171, s)-Nets in Base 3

(171−40, 171, 464)-Net over F₃ — Constructive and digital

Digital (131, 171, 464)-net over F₃, using

1 times m-reduction [i] based on digital (131, 172, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 43, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(171−40, 171, 971)-Net over F₃ — Digital

Digital (131, 171, 971)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−40, 171, 49830)-Net in Base 3 — Upper bound on s

There is no (131, 171, 49831)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3871 373858 175299 732859 197281 836558 996691 496320 383111 900840 209464 551650 823584 366937 > 3¹⁷¹ [i]