  Maximum distance separable (MDS) codes are widely used in storage systems to
protect against disk (node) failures. A node is said to have capacity $l$ over
some field $\mathbb{F}$, if it can store that amount of symbols of the field.
An $(n,k,l)$ MDS code uses $n$ nodes of capacity $l$ to store $k$ information
nodes. The MDS property guarantees the resiliency to any $n-k$ node failures.
An \emph{optimal bandwidth} (resp. \emph{optimal access}) MDS code communicates
(resp. accesses) the minimum amount of data during the repair process of a
single failed node. It was shown that this amount equals a fraction of
$1/(n-k)$ of data stored in each node. In previous optimal bandwidth
constructions, $l$ scaled polynomially with $k$ in codes with asymptotic rate
$<1$. Moreover, in constructions with a constant number of parities, i.e. rate
approaches 1, $l$ is scaled exponentially w.r.t. $k$. In this paper, we focus
on the later case of constant number of parities $n-k=r$, and ask the following
question: Given the capacity of a node $l$ what is the largest number of
information disks $k$ in an optimal bandwidth (resp. access) $(k+r,k,l)$ MDS
code. We give an upper bound for the general case, and two tight bounds in the
special cases of two important families of codes. Moreover, the bounds show
that in some cases optimal-bandwidth code has larger $k$ than optimal-access
code, and therefore these two measures are not equivalent.
