  Covariate-adaptive randomization is widely employed to balance baseline
covariates in interventional studies such as clinical trials and experiments in
development economics. Recent years have witnessed substantial progress in
inference under covariate-adaptive randomization with a fixed number of strata.
However, concerns have been raised about the impact of a large number of strata
on its design and analysis, which is a common scenario in practice, such as in
multicenter randomized clinical trials. In this paper, we propose a general
framework for inference under covariate-adaptive randomization, which extends
the seminal works of Bugni et al. (2018, 2019) by allowing for a diverging
number of strata. Furthermore, we introduce a novel weighted regression
adjustment that ensures efficiency improvement. On top of establishing the
asymptotic theory, practical algorithms for handling situations involving an
extremely large number of strata are also developed. Moreover, by linking
design balance and inference robustness, we highlight the advantages of
stratified block randomization, which enforces better covariate balance within
strata compared to simple randomization. This paper offers a comprehensive
landscape of inference under covariate-adaptive randomization, spanning from
fixed to diverging to extremely large numbers of strata.
