  We study odd-dimensional modular tensor categories and maximally non-self
dual (MNSD) modular tensor categories of low rank. We give lower bounds for the
ranks of modular tensor categories in terms of the rank of the adjoint
subcategory and the order of the group of invertible objects. As an application
of these results, we prove that MNSD modular tensor categories of ranks 13 and
15 are pointed. In addition, we show that MNSD tensor categories of ranks 17,
19, 21 and 23 are either pointed or perfect.
