  Minimax designs provide a uniform coverage of a design space $\mathcal{X}
\subseteq \mathbb{R}^p$ by minimizing the maximum distance from any point in
this space to its nearest design point. Although minimax designs have many
useful applications, e.g., for optimal sensor allocation or as space-filling
designs for computer experiments, there has been little work in developing
algorithms for generating these designs, due to its computational complexity.
In this paper, a new hybrid algorithm combining particle swarm optimization and
clustering is proposed for generating minimax designs on any convex and bounded
design space. The computation time of this algorithm scales linearly in
dimension $p$, meaning our method can generate minimax designs efficiently for
high-dimensional regions. Simulation studies and a real-world example show that
the proposed algorithm provides improved minimax performance over existing
methods on a variety of design spaces. Finally, we introduce a new type of
experimental design called a minimax projection design, and show that this
proposed design provides better minimax performance on projected subspaces of
$\mathcal{X}$ compared to existing designs. An efficient implementation of
these algorithms can be found in the R package minimaxdesign.
