  We prove that under very mild conditions for any interpolation formula $f(x)
= \sum_{\lambda\in \Lambda} f(\lambda)a_\lambda(x) + \sum_{\mu\in M}
\hat{f}(\mu)b_{\mu}(x)$ we have a lower bound for the counting functions
$n_\Lambda(R_1) + n_{M}(R_2) \ge 4R_1R_2 - C\log^{2+\varepsilon}(4R_1R_2)$
which very closely matches interpolation formulas discovered by Radchenko and
Viazovska and by Bondarenko, Radchenko and Seip.
