关于LD设计的一个递归构造

A RECURRENCE CONSTRUCTION FOR LD-DESIGNS

§1.引言 陆家羲在[1]的Ⅲ中引入一种组合设计——LD设计.为进一步研究LD设计,又提出LD设计.以下是它们的定义. 设X是一个n元集,称满足如下条件的集族.

In this paper, we give a recurrence theorem of LD~*-design, which was firstintroduced by [1]. On the basis of Theorem 6A provided in Ⅲ of [1], we co-nstructively prove that if q is a prime power greater than 4 and 1 + n ∈D~*,and if there exists a pair of orthogonal Latin squares of order n, then 1 +qn ∈ D~*.