  In this short note we will prove that non-vanishing determinant (NVD)
criterion is not enough for an asymmetric space-time block code (STBC) to
achieve the optimal diversity-multiplexing gain trade-off (DMT). This result is
in contrast to the recent result made by Srinath and Rajan. In order to clarify
the issue further the approximately universality criterion by Tavildar and
Viswanath is translated into language of lattice theory and some conjectures
are given.
