MinT - Best Known (212−65, 212, s)-Nets in Base 3

Best Known (212−65, 212, s)-Nets in Base 3

(212−65, 212, 204)-Net over F₃ — Constructive and digital

Digital (147, 212, 204)-net over F₃, using

1 times m-reduction [i] based on digital (147, 213, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 71, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(212−65, 212, 435)-Net over F₃ — Digital

Digital (147, 212, 435)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−65, 212, 8919)-Net in Base 3 — Upper bound on s

There is no (147, 212, 8920)-net in base 3, because

1 times m-reduction [i] would yield (147, 211, 8920)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47139 227138 829129 309147 575456 828977 747787 948143 525027 916957 550270 453499 217666 550863 106465 486470 150145 > 3²¹¹ [i]