Absolute bounds on the number of generators of Cohen-Macaulay ideals of height at most 2

For a Noetherian local domain $A$, there exists an upper bound $N_{\tau }(A)$ on the minimal number of generators of any height two ideal $I$ for which $A\mathrm{/}I$ is Cohen-Macaulay of type $\tau$. More precisely, we may take $N_{\tau }(A):=(\tau +1)e_{\text{h}}(A)$, where $e_{\text{h}}(A)$ is the homological multiplicity of $A$.