Quasi-complementary sequence sets (QCSSs) play an important role in multi-carrier code division multiple access (MC-CDMA) systems as they can support more users than perfect complementary sequence sets (PCSSs). The objective of this paper is to present new constructions of asymptotically optimal periodic and aperiodic QCSSs with large set sizes. Firstly, we construct a family of asymptotically optimal periodic $(p^{2n}, p^n-1, p^n-1, p^n+1)$ QCSSs with small alphabet size $p$, which has larger set size than the known family of periodic $(p^n(p^n-1), p^n-1, p^n-1, p^n+1)$ QCSSs. Secondly, we construct five new families of asymptotically optimal aperiodic QCSSs with large set sizes and low aperiodic tolerances. Each family of these aperiodic QCSSs has set size $\Theta(K^2)$ for some flock size $K$. Compared with known asymptotically optimal aperiodic QCSSs in the literature, the proposed aperiodic QCSSs by us have better parameters or new lengths of their constituent sequences.

翻译：准互补序列集(QCSSs)在多载波码分多址(MC-CDMA)系统中扮演重要角色，因其能比完美互补序列集(PCSSs)支持更多用户。本文旨在提出具有大规模集合尺寸的渐近最优周期与非周期QCSSs的新构造方法。首先，我们构造了一族具有小字母表尺寸$p$的渐近最优周期$(p^{2n}, p^n-1, p^n-1, p^n+1)$ QCSSs，其集合尺寸大于已知的周期$(p^n(p^n-1), p^n-1, p^n-1, p^n+1)$ QCSSs族。其次，我们构造了五族具有大规模集合尺寸与低非周期容限的渐近最优非周期QCSSs。每一族非周期QCSSs对于特定群集尺寸$K$均具有$\Theta(K^2)$量级的集合尺寸。与文献中已知的渐近最优非周期QCSSs相比，本文提出的非周期QCSSs在参数性能或组成序列的长度新颖性方面具有更优表现。