lower bound

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 \subsection{D-Optimality Criterion}
+Ideally, motivated by the $D$-optimality criterion, we would like to design a mechanism that maximizes \eqref{dcrit} within a good approximation ratio. As \eqref{dcrit} may take arbitrarily small negative values, to define a meaningful approximation we consider with the (equivalent) maximization of $V(S) = f(\det\T{X_S}X_S )$, for some increasing, on-to function $f:\reals_+\to\reals_+$. However, the following lower bound implies that such an optimization goal cannot be attained under the costraints of  truthfulness, budget feasibility, and individional rationallity.
+
 \begin{lemma}
-For any $M>0$, there is no truthful, budget feasible, individionally rational mechanism for optimal mechanism design with value fuction $V(S) = \det{\T{X_S}X_S}$.
+For any $M>1$, there is no truthful, budget feasible, individionally rational mechanism for optimal mechanism design with value fuction $V(S) = \det{\T{X_S}X_S}$.
 \end{lemma}
 \begin{proof}
 \input{proof_of_lower_bound1}