Can the measurement matrix used for compressive sensing be a sparse matrix?

Can the measurement matrix used for compressive sensing be a sparse matrix?

I am interested in analyzing Compressive Mechanism: Utilizing Sparse
Representation in Differential Privacy. In my research, the measurement
matrix $A\mathbb \in R^{m \times n}$ needs to be sparse. The problem is
that $n$ is potentially huge, for instance, it may be greater than
$50,000,000,000$. Hence, sparsity is necessary if the matrix is going to
be represented in memory. Using single-precision floating point numbers,
where $m=\Theta(\log(n))$, a dense matrix will need more than 6000
gigabytes of memory!
I tried looking up sparse constructions for the measurement matrix but it
does not google well; the word "sparse" is pretty common in compressive
sensing literature. Also I discovered that the Restricted Isometry
Property is not the only property that is sufficient for compressive
sensing [2], rendering the search even harder.
For my purposes, it would be equally good to find a sparse construction
for the measurement matrix, or alternatively finding out that such a
construction is computationally infeasible (NP-hard, in the spirit of [3]
and [4]), so I can dismiss this method altogether.
[2] B.S. Kashin and V.N.Temlyakov, A Remark on Compressed Sensing
[3] Afonso S. Bandeira, Edgar Dobriban, Dustin G. Mixon, William F. Sawin,
Certifying the Restricted Isometry Property is Hard
[4] Andreas M. Tillmann, Marc E. Pfetsch, The Computational Complexity of
the Restricted Isometry Property, the Nullspace Property, and Related
Concepts in Compressed Sensing