Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution. Existing constructions rely on circular population sequences, which restrict the design space by forcing samples to be contiguous blocks of a sequence. We propose a new construction based on minimum tactical configurations that removes this topological constraint. The resulting designs are fixed-size, have equal inclusion probabilities, and belong to the class with minimum feasible configuration size. We develop both a simple initialization valid for arbitrary population and sample sizes and a spatial initialization that yields a lower initial expected discrepancy, together with a simulated annealing algorithm for optimization within this class. In simulations and empirical examples, the proposed method outperforms state-of-the-art alternatives in terms of distributional fit, balance, and spatial spread.

翻译：分布平衡抽样设计是一类低差异概率设计，通过最小化随机样本的辅助变量分布与目标总体分布之间的期望差异来获得。现有构造方法依赖于圆形总体序列，这迫使样本成为序列中的连续块，从而限制了设计空间。我们提出了一种基于最小策略配置的新构造方法，消除了这一拓扑约束。所得设计具有固定规模、等包含概率，并属于最小可行配置规模类别。我们开发了一种适用于任意总体和样本规模的简单初始化方法，以及一种能产生更低初始期望差异的空间初始化方法，同时结合模拟退火算法在该类别内进行优化。在模拟和实证案例中，所提方法在分布拟合度、平衡性和空间散布性方面均优于现有最优替代方案。