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

Asymptotically Optimal and Near-optimal Aperiodic Quasi-Complementary Sequence Sets Based on Florentine Rectangles