  This paper considers coding for so-called partially stuck memory cells. Such
memory cells can only store partial information as some of their levels cannot
be used due to, e.g., wear out. First, we present a new code construction for
masking such partially stuck cells while additionally correcting errors. This
construction (for cells with $q >2$ levels) is achieved by generalizing an
existing masking-only construction in [1] (based on binary codes) to correct
errors as well. Compared to previous constructions in [2], our new construction
achieves larger rates for many sets of parameters. Second, we derive a
sphere-packing (any number of $u$ partially stuck cells) and a
Gilbert-Varshamov bound ($u<q$ partially stuck cells) for codes that can mask a
certain number of partially stuck cells and correct errors additionally. A
numerical comparison between the new bounds and our previous construction of
PSMCs for the case $u<q$ in [2] shows that our construction lies above the
Gilbert-Varshamov-like bound for several code parameters.
