TITLE: Is there a bound on the growth of homotopy groups of spheres?
QUESTION [7 upvotes]: That is to say, can one find a good bound on $|\pi_i(S^n)|$? Let us assume that $i\ge 2n$ to avoid all infinite quantities. Particularly, I am interested to see if there is a bound of exponential type. I do not see a way to do this though.

REPLY [5 votes]: There are relevant estimates in the 1986 paper by Hans-Werner Henn.
Hans-Werner Henn, MR 850372 On the growth of homotopy groups, Manuscripta Math. 56 (1986), no. 2, 235--245.