MinT - Best Known (197−83, 197, s)-Nets in Base 3

Best Known (197−83, 197, s)-Nets in Base 3

(197−83, 197, 128)-Net over F₃ — Constructive and digital

Digital (114, 197, 128)-net over F₃, using

5 times m-reduction [i] based on digital (114, 202, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 101, 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]

(197−83, 197, 159)-Net over F₃ — Digital

Digital (114, 197, 159)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−83, 197, 1500)-Net in Base 3 — Upper bound on s

There is no (114, 197, 1501)-net in base 3, because

1 times m-reduction [i] would yield (114, 196, 1501)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3299 333550 720798 693766 260256 243356 676384 279601 242808 520474 571172 533582 251992 533890 584795 844123 > 3¹⁹⁶ [i]