MinT - Best Known (53, 53+35, s)-Nets in Base 3

Best Known (53, 53+35, s)-Nets in Base 3

(53, 53+35, 80)-Net over F₃ — Constructive and digital

Digital (53, 88, 80)-net over F₃, using

2 times m-reduction [i] based on digital (53, 90, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 45, 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]

(53, 53+35, 97)-Net over F₃ — Digital

Digital (53, 88, 97)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+35, 975)-Net in Base 3 — Upper bound on s

There is no (53, 88, 976)-net in base 3, because

1 times m-reduction [i] would yield (53, 87, 976)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 323603 480899 366420 010921 140120 102311 853473 > 3⁸⁷ [i]