  Quasi-complementary sequence sets (QCSSs) can be seen as a generalized
version of complete complementary codes (CCCs), which enables multicarrier
communication systems to support more users. The contribution of this work is
two-fold. First, we propose a systematic construction of Florentine rectangles.
Secondly, we propose several sets of CCCs and QCSS, using Florentine
rectangles. The CCCs and QCSS are constructed over $\mathbb{Z}_N$, where
$N\geq2$ is any integer. The cross-correlation magnitude of any two of the
constructed CCCs is upper bounded by $N$. By combining the proposed CCCs, we
propose asymptotically optimal and near-optimal QCSSs with new parameters. This
solves a long-standing problem, of designing asymptotically optimal aperiodic
QCSS over $\mathbb{Z}_N$, where $N$ is any integer.
