The heuristic all-colluders-caught estimate for fingerprinting

Let $n$ users receive binary codewords of length $\ell$, let $\mathcal{C}$ be the colluder set of size $c$, and let $\mathcal{C}'$ be the set of accused users under the decoder of Theorem 1. Let $\varepsilon_1,\varepsilon_2>0$ and replace the parameter $\gamma$ in that theorem by

$$\gamma' = \frac{\ln(c/\varepsilon_2)}{\ln(n/\varepsilon_1)}.$$

All-colluders-caught estimate. With probability at least $1-\varepsilon_1$, no innocent users are accused, and with probability at least $1-\varepsilon_2$, all colluders are caught, meaning $\mathcal{C}'$ contains $\mathcal{C}$. This is presented as a heuristic estimate for the code length needed to catch every colluder; the source does not establish it as a theorem, so its status remains open.