MinT - Best Known (120, 120+81, s)-Nets in Base 3

Best Known (120, 120+81, s)-Nets in Base 3

(120, 120+81, 148)-Net over F₃ — Constructive and digital

Digital (120, 201, 148)-net over F₃, using

5 times m-reduction [i] based on digital (120, 206, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 103, 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]

(120, 120+81, 184)-Net over F₃ — Digital

Digital (120, 201, 184)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+81, 1876)-Net in Base 3 — Upper bound on s

There is no (120, 201, 1877)-net in base 3, because

1 times m-reduction [i] would yield (120, 200, 1877)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 267214 987389 955416 305613 262873 929995 223484 140174 645214 939308 464610 434307 296838 168016 270068 020961 > 3²⁰⁰ [i]