MinT - Best Known (165, 165+73, s)-Nets in Base 3

Best Known (165, 165+73, s)-Nets in Base 3

(165, 165+73, 228)-Net over F₃ — Constructive and digital

Digital (165, 238, 228)-net over F₃, using

3¹ times duplication [i] based on digital (164, 237, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 79, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(165, 165+73, 481)-Net over F₃ — Digital

Digital (165, 238, 481)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+73, 9844)-Net in Base 3 — Upper bound on s

There is no (165, 238, 9845)-net in base 3, because

1 times m-reduction [i] would yield (165, 237, 9845)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 119812 399049 406178 415442 057650 182486 254092 295175 193114 140169 116000 721448 133349 399215 211144 587117 664795 619103 186513 > 3²³⁷ [i]