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In this paper, we construct inequivalent Hadamard matrices based on Yang multiplication methods for base sequences which are obtained from near normal sequences. This has been achieved by employing various Unix tools and sophisticated techniques, such as metaprogramming. In addition, we present a classification for near normal sequences of length \( 4n + 1 \), for \( n \leq 11 \) and some of these for \( n = 12, 13, 14, 15 \), taking into account previously known results. Finally, we improve several constructive lower bounds for inequivalent Hadamard matrices of large orders.