  In this paper, we study a more general version of multidimensional Bohr radii
for the holomorphic functions defined on unit ball of $\ell^n_q\,\,(1\leq q\leq
\infty)$ spaces with values in arbitrary complex Banach spaces. More precisely,
we study the multidimensional Bohr radii for bounded linear operators between
complex Banach spaces, primarily motivated by the work of A. Defant, M.
Maestre, and U. Schwarting [Adv. Math. 231 (2012), pp. 2837--2857]. We obtain
the exact asymptotic estimates of multidimensional Bohr radius for both finite
and infinite dimensional Banach spaces. As an application, we find the lower
bound of arithmetic Bohr radius.
