MinT - Best Known (199−47, 199, s)-Nets in Base 3

Best Known (199−47, 199, s)-Nets in Base 3

(199−47, 199, 464)-Net over F₃ — Constructive and digital

Digital (152, 199, 464)-net over F₃, using

1 times m-reduction [i] based on digital (152, 200, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 50, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(199−47, 199, 1066)-Net over F₃ — Digital

Digital (152, 199, 1066)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−47, 199, 60347)-Net in Base 3 — Upper bound on s

There is no (152, 199, 60348)-net in base 3, because

1 times m-reduction [i] would yield (152, 198, 60348)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29523 284084 243763 111445 356637 273869 393669 433732 223900 301300 647073 990808 866992 267754 701049 432081 > 3¹⁹⁸ [i]