Abstract: We study experimental design under network interference, a setting that arises in many applications such as medical and epidemiological interventions, political science field experiments, and online marketplace experiments. Under network interference, the outcome of a unit may depend on its own treatment and the treatments of its neighbors in a given interference graph. Our goal is to estimate the global average treatment effect, defined as the contrast between all units treated and all units in control. For any experimental design, understood as a joint distribution over treatment assignments, one can construct a Horvitz–Thompson estimator that directly incorporates the graph structure and is unbiased for the estimand. We consider the problem of choosing a design that minimizes the worst case variance of this estimator, where the worst case is taken over all potential outcome models with $ell_2$ norms bounded by $Csqrt{n}$. We first establish a lower bound: up to logarithmic factors, any design must incur worst case variance at least $Omega(d/n)$, where $d$ is the maximum degree of the interference graph. We then study a broad class of pseudo-random interference graphs, characterized by controlled codegree conditions, and show that this lower bound is tight. In particular, we construct a simple design that samples a random subset of nodes and assigns treatment to each selected node and its neighbors, and we show that its worst case variance is $O(d/n)$, again up to logarithmic factors. Together, the results show that for pseudo-random interference graphs the minimax rate for estimating the global average treatment effect is $Theta(d/n)$. This is joint work with Shuangping Li from Yale University.