This paper studies a two-stage model of experimentation, where the researcher first samples representative experimental participants from an eligible pool, then assigns each sampled unit to treatment or control, using matched $k$-tuples randomization at both stages. To implement such designs, we develop a fast new algorithm for matching units into $k$-tuples for any $k \ge 2$ and any dimension of covariates. By surveying 200 recent experimental working papers, we estimate that our algorithm newly enables multivariate fine stratification with provable match quality guarantees for about 44\% of experiments in economics. We show that finely stratified sampling and assignment both nonparametrically reduce the variance of treatment effect estimation, with the gains from stratified sampling increasing in the size of the eligible pool and how well covariates predict treatment effect heterogeneity. We develop new inference methods that fully exploit the efficiency gains from both design stages, allowing researchers to report smaller standard errors if they designed a representative experiment. An application to nine published experiments quantifies the efficiency gains.