MinT - Best Known (172−74, 172, s)-Nets in Base 3

Best Known (172−74, 172, s)-Nets in Base 3

(172−74, 172, 80)-Net over F₃ — Constructive and digital

Digital (98, 172, 80)-net over F₃, using

8 times m-reduction [i] based on digital (98, 180, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 90, 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]

(172−74, 172, 134)-Net over F₃ — Digital

Digital (98, 172, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−74, 172, 1174)-Net in Base 3 — Upper bound on s

There is no (98, 172, 1175)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11921 909618 378985 180199 282184 392324 441434 850382 443082 796397 031610 542405 472600 396455 > 3¹⁷² [i]