MinT - Best Known (240−56, 240, s)-Nets in Base 3

Best Known (240−56, 240, s)-Nets in Base 3

(240−56, 240, 600)-Net over F₃ — Constructive and digital

Digital (184, 240, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 60, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(240−56, 240, 1308)-Net over F₃ — Digital

Digital (184, 240, 1308)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−56, 240, 69408)-Net in Base 3 — Upper bound on s

There is no (184, 240, 69409)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 229663 451381 622116 708496 615213 438016 809158 418800 913254 320296 063964 797371 557780 181615 196152 126222 944833 080348 312625 > 3²⁴⁰ [i]