MinT - Best Known (237−103, 237, s)-Nets in Base 3

Best Known (237−103, 237, s)-Nets in Base 3

(237−103, 237, 128)-Net over F₃ — Constructive and digital

Digital (134, 237, 128)-net over F₃, using

5 times m-reduction [i] based on digital (134, 242, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 121, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(237−103, 237, 172)-Net over F₃ — Digital

Digital (134, 237, 172)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−103, 237, 1552)-Net in Base 3 — Upper bound on s

There is no (134, 237, 1553)-net in base 3, because

1 times m-reduction [i] would yield (134, 236, 1553)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40868 494842 804042 255208 424393 347189 840348 487983 174331 186519 796498 627680 227659 331249 300707 327588 798867 668990 499099 > 3²³⁶ [i]