MinT - Best Known (152−56, 152, s)-Nets in Base 3

Best Known (152−56, 152, s)-Nets in Base 3

(152−56, 152, 148)-Net over F₃ — Constructive and digital

Digital (96, 152, 148)-net over F₃, using

6 times m-reduction [i] based on digital (96, 158, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 79, 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]

(152−56, 152, 187)-Net over F₃ — Digital

Digital (96, 152, 187)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−56, 152, 2170)-Net in Base 3 — Upper bound on s

There is no (96, 152, 2171)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 337723 552019 114940 759577 623736 946197 009259 292396 931494 430041 863539 960745 > 3¹⁵² [i]