We give a novel lower bound of the minimum values of the normalized auto-correlation functions for de Bruijn sequences of length N=2ⁿ(n≥3). The lower bound is tight in the sense that the equality holds for n=3 and n=4. For 3≤n≤6, we experimentally characterize the worst and the second-worst sequences in all de Brujin sequences in terms of the normalized auto-correlation function.