MinT - Best Known (210−97, 210, s)-Nets in Base 3

Best Known (210−97, 210, s)-Nets in Base 3

(210−97, 210, 80)-Net over F₃ — Constructive and digital

Digital (113, 210, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 105, 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]

(210−97, 210, 130)-Net over F₃ — Digital

Digital (113, 210, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−97, 210, 1073)-Net in Base 3 — Upper bound on s

There is no (113, 210, 1074)-net in base 3, because

1 times m-reduction [i] would yield (113, 209, 1074)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 5378 187036 148444 546080 179879 357872 489981 484135 323768 166388 508899 443022 225969 024957 932575 574720 290785 > 3²⁰⁹ [i]