Derandomization By Conditional Probabilities And Its Applications To (m,4)-Splitting System

An (m, t)-splitting system is a pair of (X,B) where m and t are integers and0<t≤m, X is a finite set of points and|X|=m, B is a collection of subsets of X called blocks, for every Y(?)X and|y|=t, there exists a block B(?)b such that|B∩y|=[t/2]. If every block B(?)b has the size of [m/2], it is a uniform splitting system.The probabilistic method is a powerful tool for tackling many problems in discrete mathematics, By which we can get the existing result of the combinational problems. But in general, this method is sometimes non-constructing method. In this paper, we use derandomization by conditional probabilities to apply to (m,4)-splitting system, we will also give an efficient algorithm to construct the array. We have programmed for the algorithm, and have done some experiments to verify the validities of the algorithm. The analysis for the results is also given. At the end of the paper, we give the constructing results.