  In a recent note F. Lin showed that if a rational homology sphere $Y$ admits
a taut foliation then the Heegaard Floer module $HF^-(Y)$ contains a copy of
$\mathbf{F}[U]/U$ as a summand (arXiv:2309.01222). This implies that either the
$L$-space conjecture is false or that Heegaard Floer homology satisfies a
geography restriction. We verify that Lin's geography restriction holds for a
wide class of rational homology spheres. Indeed, we show that the Heegaard
Floer module $HF^-(Y)$ may satisfy a stronger geography restriction.
