MinT - Best Known (178, 230, s)-Nets in Base 3

Best Known (178, 230, s)-Nets in Base 3

(178, 230, 640)-Net over F₃ — Constructive and digital

Digital (178, 230, 640)-net over F₃, using

3² times duplication [i] based on digital (176, 228, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 57, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(178, 230, 1433)-Net over F₃ — Digital

Digital (178, 230, 1433)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178, 230, 87664)-Net in Base 3 — Upper bound on s

There is no (178, 230, 87665)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 692360 413043 792619 981882 367092 427852 087856 795265 902988 163058 051195 261199 257452 998165 630862 440699 325281 719625 > 3²³⁰ [i]