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Dietzfelbinger, Hromkovi\\v{c}, and Schnitger (1996) showed that n \\le (\\rk M)^2, regardless of over which field the rank is computed, and asked whether the exponent on \\rk M can be improved.\n  We settle this question for nonzero characteristic by constructing a family of matrices for which the bound is asymptotically tight. 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