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The Chebotarev invariant $C(G)$ of $G$ is the expected value of the random variable $n$ that is minimal subject to the requirement that $n$ randomly chosen elements of $G$ invariably generate $G$. The authors recently showed that for each $\\epsilon>0$, there exists a constant $c_{\\epsilon}$ such that $C(G)\\le (1+\\epsilon)\\sqrt{|G|}+c_{\\epsilon}$. This bound is asymptotically best possible. 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