Massey's same-cluster query lower-bound conjecture

Let $k=2$, let $\bfX\in\{0,1\}^n$ be the label vector, and let a querying scheme use $m$ same cluster' queries, each involving two elements ($\Delta=2$). A scheme is **$(1-\delta)$-good** if it correctly recovers at least $(1-\delta)n$ labels for every label vector. **Massey's conjecture.** Any $(1-\delta)$-good scheme with $m$ same cluster' queries must satisfy

$$\delta \ge p\left(1-\frac{m}{nH(p)}\right).$$

The conjecture concerns the inefficiency of linear, same-cluster queries for approximate recovery and is presented as a reformulation of a conjecture by Massey, motivated by the limitation of linear codes as rate-distortion codes. Its resolution is not specified in the source.