Minimal critical exponent of quasiperiodic words

A quasiperiodic word is a finite or infinite word that can be obtained by concatenations or overlaps of a given finite word. We proved that the least critical exponent of a quasiperiodic binary word is 73. For larger alphabets, given any ϵ>0ϵ>0, we provide a construction of a ternary quasiperiodic word with critical exponent 2+ϵ2+ϵ.