MinT - Best Known (229−56, 229, s)-Nets in Base 3

Best Known (229−56, 229, s)-Nets in Base 3

(229−56, 229, 400)-Net over F₃ — Constructive and digital

Digital (173, 229, 400)-net over F₃, using

3¹ times duplication [i] based on digital (172, 228, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 57, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(229−56, 229, 1037)-Net over F₃ — Digital

Digital (173, 229, 1037)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−56, 229, 45069)-Net in Base 3 — Upper bound on s

There is no (173, 229, 45070)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 237539 663864 109973 135119 429427 163718 360113 859087 775465 244093 093705 098796 566839 289625 136652 432512 520653 238137 > 3²²⁹ [i]