For measures with polylogarithmic Fourier decay and expanding integer matrix sequences, the number of hits of the orbit on shrinking boxes equals the expected count up to an error of order Ψ(N)^(d/(d+1)) (log Ψ(N))^(2+ε).
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Quantitative Matrix-Driven Diophantine approximation on $M_0$-sets
For measures with polylogarithmic Fourier decay and expanding integer matrix sequences, the number of hits of the orbit on shrinking boxes equals the expected count up to an error of order Ψ(N)^(d/(d+1)) (log Ψ(N))^(2+ε).