MinT - Best Known (180−39, 180, s)-Nets in Base 3

Best Known (180−39, 180, s)-Nets in Base 3

(180−39, 180, 640)-Net over F₃ — Constructive and digital

Digital (141, 180, 640)-net over F₃, using

t-expansion [i] based on digital (140, 180, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 45, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(180−39, 180, 1386)-Net over F₃ — Digital

Digital (141, 180, 1386)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−39, 180, 123909)-Net in Base 3 — Upper bound on s

There is no (141, 180, 123910)-net in base 3, because

1 times m-reduction [i] would yield (141, 179, 123910)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25 393811 355949 202749 348310 053100 837104 437963 665372 649336 195680 172607 221586 833890 607681 > 3¹⁷⁹ [i]