MinT - Best Known (159−62, 159, s)-Nets in Base 3

Best Known (159−62, 159, s)-Nets in Base 3

(159−62, 159, 148)-Net over F₃ — Constructive and digital

Digital (97, 159, 148)-net over F₃, using

1 times m-reduction [i] based on digital (97, 160, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 80, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(159−62, 159, 165)-Net over F₃ — Digital

Digital (97, 159, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−62, 159, 1708)-Net in Base 3 — Upper bound on s

There is no (97, 159, 1709)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7385 033481 093574 633695 966272 209980 036970 710710 375047 088181 245442 431735 101275 > 3¹⁵⁹ [i]