Asymptotically Optimal Quasi-Complementary Code Sets of Length $p_{1}^{m_{1}}p_{2}^{m_{2}}$

In this paper we propose a construction of quasi-complementary code sets (QCCSs) of length
$p_{1}^{m_{1}}p_{2}^{m_{2}}$
, where
$p_{1},p_{2}$
are primes and
$m_{1}, m_{2}$
are positive integers, and show that the proposed QCCSs achieve optimality asymptotically. The construction generalizes a recent work by Sarkar et al. on QCCSs of length
$p^{m}$
, which has more flexible alphabet size.