  We examine the set of objects which can be built in type IIA string theory by
matrix methods using an infinite number of D0-branes. In addition to stacks of
ordinary Dp-branes and branes in background fields, we find exotic states which
cannot be constructed by other means. These states exhibit strongly
noncommutative geometry, (e.g., partial derivatives on them do not commute) and
some are conjectured to have Z_N-valued charges similar to those of the type I
D-instanton. Real-valued charges are forbidden by Dirac quantization, leading
to a nontrivial relationship between noncommutative topological invariants.
