MinT - Best Known (188, 188+54, s)-Nets in Base 3

Best Known (188, 188+54, s)-Nets in Base 3

(188, 188+54, 640)-Net over F₃ — Constructive and digital

Digital (188, 242, 640)-net over F₃, using

2 times m-reduction [i] based on digital (188, 244, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 61, 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]

(188, 188+54, 1580)-Net over F₃ — Digital

Digital (188, 242, 1580)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(188, 188+54, 103201)-Net in Base 3 — Upper bound on s

There is no (188, 242, 103202)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 068084 908455 609799 309354 273571 935718 227597 186252 179032 035075 487801 399765 851864 909460 186876 182793 624709 185780 431969 > 3²⁴² [i]