  We prove that the `connective constant' for ternary square-free words is at
least $2^{1/17} = 1.0416 ... $, improving on Brinkhuis and Brandenburg's lower
bounds of $2^{1/24}=1.0293 ...$ and $2^{1/22}=1.032 ...$ respectively. This is
the first improvement since 1983.
