MinT - Best Known (167, 247, s)-Nets in Base 3

Best Known (167, 247, s)-Nets in Base 3

(167, 247, 172)-Net over F₃ — Constructive and digital

Digital (167, 247, 172)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (13, 53, 24)-net over F₃, using
  - net from sequence [i] based on digital (13, 23)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
      - a function field by SÃ©mirat [i]
2. digital (114, 194, 148)-net over F₃, using
  - trace code for nets [i] based on digital (17, 97, 74)-net over F₉, using
    - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
        a function field by GarcÃa and Quoos [i]

(167, 247, 418)-Net over F₃ — Digital

Digital (167, 247, 418)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 247, 6926)-Net in Base 3 — Upper bound on s

There is no (167, 247, 6927)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7077 957061 109799 701276 960886 061243 818209 253905 153980 081548 000494 143283 959865 422398 210842 448180 742902 773541 186958 334129 > 3²⁴⁷ [i]