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We ask what is the probability that for all $1\\leq l\\leq p$ and $x,y\\in W_l$, \\[\n  \\|x-y\\|_2\\leq\\|Hx-Hy\\|_2\\leq D\\|x-y\\|_2. \\] We show that for $m=O\\big(k+\\frac{\\ln{p}}{\\ln{D}}\\big)$ and a variety of different classes of random matrices $H$, which include the class of Gaussian matrices, existence is assured and the probability is very high. 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