  For any rational number $h$ and all sufficiently large $n$ we give a
deterministic construction for an $n\times \lfloor hn\rfloor$ compressed
sensing matrix with $(\ell_1,t)$-recoverability where $t=O(\sqrt{n})$. Our
method uses pairwise balanced designs and complex Hadamard matrices in the
construction of $\epsilon$-equiangular frames, which we introduce as a
generalisation of equiangular tight frames. The method is general and produces
good compressed sensing matrices from any appropriately chosen pairwise
balanced design. The $(\ell_1,t)$-recoverability performance is specified as a
simple function of the parameters of the design. To obtain our asymptotic
existence result we prove new results on the existence of pairwise balanced
designs in which the numbers of blocks of each size are specified.
