Banach–Mazur nondensifiability number

In the present paper, based on the so called degree of nondensifiability (DND), we introduce the concept of Banach–Mazur nondensifiability number of two given Banach spaces and prove that such a number is an optimal lower bound for the well known Banach–Mazur distance. For a given infinite dimensional Banach space, we also introduce a new constant. We demonstrate a relationship between this constant and the Banach–Mazur distance.