  We consider a coded caching system in which some users are offline at the
time of delivery. Such systems are called hotplug coded caching systems. A
placement delivery array (PDA) is a well-known tool for constructing a coded
caching scheme for dedicated caches. In this paper, we introduce the concept of
PDAs for hotplug coded caching schemes and refer to it as a hotplug placement
delivery array (HpPDA). We give an algorithm to describe the placement and the
delivery phase of a hotplug coded caching scheme using HpPDA. We show that an
existing hotplug coded caching scheme given by Y. Ma and D. Tuninetti in 2022
corresponds to a class of HpPDAs and then propose a method to further improve
the rate of that scheme. Additionally, we construct a class of HpPDAs using
$t$-designs, which corresponds to a scheme for hotplug coded caching systems.
We further improve the rate of this scheme and prove that the cut-set bound is
achieved in some higher memory range for a hotplug coded caching system with
three active users.
