MinT - Best Known (152−40, 152, s)-Nets in Base 3

Best Known (152−40, 152, s)-Nets in Base 3

(152−40, 152, 282)-Net over F₃ — Constructive and digital

Digital (112, 152, 282)-net over F₃, using

1 times m-reduction [i] based on digital (112, 153, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 51, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(152−40, 152, 559)-Net over F₃ — Digital

Digital (112, 152, 559)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−40, 152, 17535)-Net in Base 3 — Upper bound on s

There is no (112, 152, 17536)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 332229 292336 060600 007029 667906 505288 380569 169088 730220 369968 071002 528769 > 3¹⁵² [i]