Asymptotic Padé Predictions up to Six Loops in QCD and Eight Loops in $λφ^4$

We assess the accuracy of our previous Asymptotic Padé predictions of the five-loop QCD $β$-function and quark mass anomalous dimension in the light of subsequent exact results. We find the low-order coefficients in an expansion in powers of $N_F$ (the number of flavours) were correct to within $1\%$. Furthermore an examination of recent results in $λφ^4$ theory indicates that the Asymptotic Padé methods deliver predictions which increase in accuracy with loop order. Encouraged by this, we present six-loop Asymptotic Padé predictions for the QCD $β$-function and quark mass anomalous dimension, and also for the eight-loop $β$-function in $O(N)$ $λφ^4$ theory.