  In this short note, we answer a question raised by M. Papikian on a universal
upper bound for the degree of the extension of $K_\infty$ given by adjoining
the periods of a Drinfeld module of rank 2. We show that contrary to the rank 1
case such a universal upper bound does not exist, and the proof generalises to
higher rank. Moreover, we give an upper and lower bound for the extension
degree depending on the valuations of the defining coefficients of the Drinfeld
module. In particular, the lower bound shows the non-existence of a universal
upper bound.
