MinT - Best Known (145−64, 145, s)-Nets in Base 3

Best Known (145−64, 145, s)-Nets in Base 3

(145−64, 145, 80)-Net over F₃ — Constructive and digital

Digital (81, 145, 80)-net over F₃, using

1 times m-reduction [i] based on digital (81, 146, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 73, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(145−64, 145, 108)-Net over F₃ — Digital

Digital (81, 145, 108)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−64, 145, 897)-Net in Base 3 — Upper bound on s

There is no (81, 145, 898)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1549 599097 179866 675843 542658 741409 585768 601600 969927 723324 308060 088641 > 3¹⁴⁵ [i]