Maximal non-attacking queens on four-sided hypercubes

A $d$-dimensional hypercube of side length $4$ is the board with vertex set $\{0,1,2,3\}^d$. Queens are non-attacking when no two occupy positions joined by a permitted queen move, and the maximal non-attacking queen set problem asks for the largest such set.

Four-sided hypercube queen conjecture. The maximal non-attacking queen set problem on a $d$-dimensional hypercube of side length $4$ has solution size

$$2^d$$

for $d\geq 4$.

This formula is inferred from computational data, including newly calculated values for higher-dimensional cases. It remains a computationally supported conjecture rather than a proved general formula.