MinT - Best Known (171−38, 171, s)-Nets in Base 3

Best Known (171−38, 171, s)-Nets in Base 3

(171−38, 171, 600)-Net over F₃ — Constructive and digital

Digital (133, 171, 600)-net over F₃, using

1 times m-reduction [i] based on digital (133, 172, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 43, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(171−38, 171, 1193)-Net over F₃ — Digital

Digital (133, 171, 1193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−38, 171, 78014)-Net in Base 3 — Upper bound on s

There is no (133, 171, 78015)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3870 933824 730457 312774 132359 709527 510876 306570 015118 377566 850599 599161 405500 831451 > 3¹⁷¹ [i]