A sampling scheme that selects a random 0–1 matrix of size $N\times M$ uniformly in the set of 0–1 matrices with predetermined row and column totals is investigated. The limits, as $M$ goes to $\infty$ and $N$ is fixed, of the column relative frequencies is derived. The limiting values give a sampling design for a population of $N$ units that generalizes the conditional Poisson sampling design introduced by Hajek. A method to calculate the joint selection probabilities for this new design using the known single inclusion probabilities is presented. Numerical examples show that the limiting theorem provides good approximations to the fixed $M$ column probabilities of a random matrix.

一种抽样方案，选择大小为0-1的随机矩阵 $ñ\times \mathrm{中号}$在具有预定行和列总计的0-1矩阵集中均匀地进行研究。极限$\mathrm{中号}$ 去 $\infty$ 和 $ñ$固定，则得出列的相对频率。极限值给出了针对以下人群的抽样设计$ñ$推广Hajek引入的条件Poisson抽样设计的单位。提出了一种使用已知的单项包含概率为该新设计计算联合选择概率的方法。数值算例表明，极限定理提供了与定值的良好近似$\mathrm{中号}$ 随机矩阵的列概率。