  This work considers the combinatorial multi-access coded caching problem
introduced in the recent work by Muralidhar \textit{et al.} [P. N. Muralidhar,
D. Katyal, and B. S. Rajan, ``Maddah-Ali-Niesen scheme for multi-access coded
caching,'' in \textit{IEEE Inf. Theory Workshop (ITW)}, 2021] The problem
setting consists of a central server having a library of $N$ files and $C$
caches each with capacity $M$. Each user in the system can access a unique set
of $r<C$ caches, and there exist users corresponding to every distinct set of
$r$ caches. Therefore, the number of users in the system is $\binom{C}{r}$. For
the aforementioned combinatorial multi-access setting, we propose a coded
caching scheme with an MDS code-based coded placement. This novel placement
technique helps to achieve a better rate in the delivery phase compared to the
optimal scheme under uncoded placement when $M> N/C$. For a lower memory
regime, we present another scheme with coded placement, which outperforms the
optimal scheme under uncoded placement if the number of files is no more than
the number of users. Further, we derive an information-theoretic lower bound on
the optimal rate-memory trade-off of the combinatorial multi-access coded
caching scheme. In addition, using the derived lower bound, we show that the
first scheme is optimal in the higher memory regime, and the second scheme is
optimal if $N\leq \binom{C}{r}$. Finally, we show that the performance of the
first scheme is within a constant factor of the optimal performance, when
$r=2$.
