  A magic rectangle of order $m\times n$ with precisely $r$ filled cells in
each row and precisely $s$ filled cells in each column, denoted $MR(m,n;r,s)$,
is an arrangement of the numbers from 0 to $mr-1$ in an $m\times n$ array such
that each number occurs exactly once in the rectangle and the sum of the
entries of each row is the same and the sum of entries of each column is also
the same. In this paper we study the existence of $MR(m,n;r,2)$,
$MR(m,km;ks,s)$, and $MR(am,bm;bs,as)$. We also prove that there exists a magic
square set $MSS(m, s; t)$ if and only if $m=s=t=1$ or $3\leq s\leq m$ and
either $s$ is even or $mt$ is odd.
