MinT - Best Known (176, 176+55, s)-Nets in Base 3

Best Known (176, 176+55, s)-Nets in Base 3

(176, 176+55, 464)-Net over F₃ — Constructive and digital

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]

(176, 176+55, 1165)-Net over F₃ — Digital

Digital (176, 231, 1165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 176+55, 63322)-Net in Base 3 — Upper bound on s

There is no (176, 231, 63323)-net in base 3, because

1 times m-reduction [i] would yield (176, 230, 63323)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 688045 701276 903272 954352 024441 245491 122833 264913 335693 519351 082414 937594 757286 005731 096619 241285 095873 445979 > 3²³⁰ [i]