MinT - Best Known (231−54, 231, s)-Nets in Base 3

Best Known (231−54, 231, s)-Nets in Base 3

(231−54, 231, 464)-Net over F₃ — Constructive and digital

Digital (177, 231, 464)-net over F₃, using

t-expansion [i] based on digital (176, 231, 464)-net over F₃, using
- 1 times m-reduction [i] based on digital (176, 232, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 58, 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]

(231−54, 231, 1258)-Net over F₃ — Digital

Digital (177, 231, 1258)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−54, 231, 65953)-Net in Base 3 — Upper bound on s

There is no (177, 231, 65954)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 076945 910089 014218 708602 875111 200750 378350 306160 461142 097802 328733 989144 748487 347847 750979 826152 587575 753313 > 3²³¹ [i]