  Over an alphabet of size 3 we construct an infinite balanced word with
critical exponent 2+sqrt(2)/2. Over an alphabet of size 4 we construct an
infinite balanced word with critical exponent (5+sqrt(5))/4. Over larger
alphabets, we give some candidates for balanced words (found computationally)
having small critical exponents. We also explore a method for proving these
results using the automated theorem prover Walnut.
