MinT - Best Known (197−47, 197, s)-Nets in Base 3

Best Known (197−47, 197, s)-Nets in Base 3

(197−47, 197, 464)-Net over F₃ — Constructive and digital

Digital (150, 197, 464)-net over F₃, using

3¹ times duplication [i] based on digital (149, 196, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 49, 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]

(197−47, 197, 1015)-Net over F₃ — Digital

Digital (150, 197, 1015)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−47, 197, 54846)-Net in Base 3 — Upper bound on s

There is no (150, 197, 54847)-net in base 3, because

1 times m-reduction [i] would yield (150, 196, 54847)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3279 501480 983954 643945 627449 121833 130936 291033 439990 726726 016406 366040 220275 460388 299907 476691 > 3¹⁹⁶ [i]