González–Zarati lower-bound conjecture for biequivariant maps

Let $\alpha(m)$ denote the number of ones in the binary expansion of $m$, and let $b(n,e)$ be the smallest positive integer $r$ for which there is a $\mathbb{Z}_{2^e}$-biequivariant map $S^{2n+1}\times S^{2n+1}\to S^{2r+1}$. González–Zarati conjecture. For $1\leq e\leq\alpha(m)$,

$$b(m+\alpha(m)-e,e)\geq 2m-\alpha(m)+e-1.$$

This conjecture gives lower bounds for biequivariant maps and, through the relationship with immersion dimensions and the topological complexity of lens spaces, would imply corresponding lower bounds for those invariants. The source presents it as a conjecture from González and Zarati; its resolution is not specified here.