Optimal augmentation size for BONuS under a subspace prior

Let $\tilde m_{\textnormal{opt}}$ be the choice of augmentation size that maximizes the power of BONuS for a subspace prior, with $m$ fixed. Assume the strong-signal regime

$$\gamma^2h^4>c.$$

Optimal augmentation-size conjecture. Under this regime,

$$\tilde m_{\textnormal{opt}}=\Theta(\sqrt{m}).$$

The preceding small-$\tilde m$ expansion has the same $1/\tilde m$ versus $\tilde m/m$ trade-off as in the point-mass case, supporting the conjectured scaling. The exact optimizer for BONuS under the subspace prior remains open.