Massive datasets present both opportunities and challenges for statistical estimation, with subsampling emerging as an effective strategy to balance statistical efficiency against computational cost. Existing approaches typically draw independent or conditionally independent subsamples, focusing on selecting individually informative observations. We propose an antithetic subsampling framework that intentionally induces negative dependence among sampled observations to reduce the variance of the resulting estimator.  Our method selects groups of observations with designed negative correlations, yielding improved estimation efficiency relative to independent subsampling. Additionally, we will present a Maximum-Variance-Reduction Stratification (MVRS) method that partitions the data to reduce the variance of subsampling estimators. MVRS incurs only a linear additional computational cost and can be seamlessly combined with existing random subsampling designs to further boost efficiency.