MinT - Best Known (135−56, 135, s)-Nets in Base 3

Best Known (135−56, 135, s)-Nets in Base 3

(135−56, 135, 80)-Net over F₃ — Constructive and digital

Digital (79, 135, 80)-net over F₃, using

7 times m-reduction [i] based on digital (79, 142, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 71, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(135−56, 135, 121)-Net over F₃ — Digital

Digital (79, 135, 121)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−56, 135, 1100)-Net in Base 3 — Upper bound on s

There is no (79, 135, 1101)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25808 563152 497547 460982 725943 828817 592914 761094 074385 720707 043377 > 3¹³⁵ [i]