摘要
设K、M为某些正整数集,X为某v元点集,G~*为某个将X划分为大小属于M的子集(称为组)的划分,A~*为X的某些大小属于K的子集(称为区组)的簇。(X,G~*,A~*)称为是一个可分组设计GD[K,λ,M;v],若X中不属于同一组的任意两点恰出现于λ个区组中。本文利用有限射影平面中的卵形,构造了一些特殊的可分组设计。
A group divisible design is a triple (X, G*, A*) satisfying (1) G* is a partition of X into subsets called groups; (2) A* is a collection of subsets of X called blocks therefore a group and a block have at most one common point; and (3) every pair of points from distinct groups occurs in exact λ blocks. In this paper, some special group divisible designs have been constructed from ovals in finite projective planes.
