  Based on a factorization of an input covariance matrix, we define a mild
generalization of an upper bound of Nikolov (2015) and Li and Xie (2020) for
the NP-Hard constrained maximum-entropy sampling problem (CMESP). We
demonstrate that this factorization bound is invariant under scaling and also
independent of the particular factorization chosen. We give a variable-fixing
methodology that could be used in a branch-and-bound scheme based on the
factorization bound for exact solution of CMESP. We report on successful
experiments with a commercial nonlinear-programming solver. We further
demonstrate that the known "mixing" technique can be successfully used to
combine the factorization bound with the factorization bound of the
complementary CMESP, and also with the "linx bound" of Anstreicher (2020).
