集合差系统的新构造

New constructions of difference systems of sets

研究集合差系统新的构造方法.借助有限域上分圆类,给出集合差系统的两个直接构造;再利用克罗内克积建立集合差系统新的递归构造,并推广了已知构造.最后应用所得到的直接构造和递归构造给出了新的渐近最优的集合差系统.

In this paper,we study new constructions of difference systems of sets.Two direct constructions of difference systems of sets are presented using cyclotomic classes over finite fields,and a new recursive construction of difference systems of sets is established using Kronecker product,which can be viewed as a generalization of the known constructions.By applying these direct and recursive constructions,some infinite series of asymptotically optimal difference systems of sets can be constructed.