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Image hashing is one of the fundamental problems that demand both efficient and effective solutions for various practical scenarios. Adversarial autoencoders are shown to be able to implicitly learn a robust, locality-preserving hash function that generates balanced and high-quality hash codes. However, the existing adversarial hashing methods are inefficient to be employed for large-scale image retrieval applications. Specifically, they require an exponential number of samples to be able to generate optimal hash codes and a significantly high computational cost to train. In this paper, we show that the high sample-complexity requirement often results in sub-optimal retrieval performance of the adversarial hashing methods. To address this challenge, we propose a new adversarial-autoencoder hashing approach that has a much lower sample requirement and computational cost. Specifically, by exploiting the desired properties of the hash function in the low-dimensional, discrete space, our method efficiently estimates a better variant of Wasserstein distance by averaging a set of easy-to-compute one-dimensional Wasserstein distances. The resulting hashing approach has an order-of-magnitude better sample complexity, thus better generalization property, compared to the other adversarial hashing methods. In addition, the computational cost is significantly reduced using our approach. We conduct experiments on several real-world datasets and show that the proposed method outperforms the competing hashing methods, achieving up to 10% improvement over the current state-of-the-art image hashing methods. The code accompanying this paper is available on Github (https://github.com/khoadoan/adversarial-hashing).