Bárány–Larman colorful topological Tverberg conjecture

Let $q \ge 2$ and $d \ge 1$ be integers. Let $C_1, \ldots, C_{d+1}$ be pairwise disjoint sets of vertices of $\Delta_{q(d+1)-1}$, each of size $q$, and let $f\colon \Delta_{q(d+1)-1} \to \mathds{R}^d$ be a continuous map. Bárány–Larman's colorful topological Tverberg conjecture. There are $q$ pairwise disjoint faces $\sigma_1, \dots, \sigma_q$ of $\Delta_{q(d+1)-1}$ such that

$$f(\sigma_1) \cap \dots \cap f(\sigma_q) \ne \emptyset$$

and each $\sigma_i$ has at most one vertex in each $C_j$. This is a colorful version of the topological Tverberg theorem beyond prime powers; it is known to be open even for affine maps, although it has been verified when $q+1$ is prime.