Most standard summaries of the literature on irrationality measure simply say, e.g., that $$ \left| \pi - \frac{p}{q}\right| > \frac{1}{q^{7.6063}} $$ for all sufficiently large $q$, without giving any indication of how large qualifies as "sufficiently large." It would occasionally be useful (for example, for my answer here) to be able to come up with explicit bounds on the size of $q$.
I don't have access to Salikhov's paper where the exponent $7.6063$ is obtained, but Hata's paper which obtained an exponent of $8.0161$ is online here. Looking through it, the proof seems to be effective (all the bounds he's using appear to be defined explicitly), but it is definitely not written to be clear about what those bounds are.
Has anyone extracted explicit bounds on the size of the denominator from any irrationality measure calculation for $\pi$ more recent than Mahler's proof (referenced in the Hata paper) that $$ \left| \pi - \frac{p}{q}\right| > \frac{1}{q^{42}} $$ unrestrictedly?
