  This paper studies a multiaccess coded caching (MACC) where the connectivity
topology between the users and the caches can be described by a class of
combinatorial designs. Our model includes as special cases several MACC
topologies considered in previous works. The considered MACC network includes a
server containing $N$ files, $\Gamma$ cache nodes and $K$ cacheless users,
where each user can access $L$ cache nodes. The server is connected to the
users via an error-free shared link, while the users can retrieve the cache
content of the connected cache-nodes while the users can directly access the
content in their connected cache-nodes. Our goal is to minimise the worst-case
transmission load on the shared link in the delivery phase. The main limitation
of the existing MACC works is that only some specific access topologies are
considered, and thus the number of users $K$ should be either linear or
exponential to $\Gamma$. We overcome this limitation by formulating a new
access topology derived from two classical combinatorial structures, referred
to as the $t$-design and the $t$-group divisible design. In these topologies,
$K$ scales linearly, polynomially, or even exponentially with $\Gamma$. By
leveraging the properties of the considered combinatorial structures, we
propose two classes of coded caching schemes for a flexible number of users,
where the number of users can scale linearly, polynomially or exponentially
with the number of cache nodes. In addition, our schemes can unify most schemes
for the shared link network and unify many schemes for the multi-access network
except for the cyclic wrap-around topology.
