摘要: G-设计是可分组设计(
GD)的推广，同时又是烛台型设计(CQS)的特例，它在四元系设计中起到重要作用。文章应用Stern和Lenz关于图因子分解的结论，通过直接构造法，得到具有三个组的G-设计
存在的充分必要条件：
。
Abstract:
As a special example of the candelabra systems (CQS),
G-design is the extension of group divisible designs (
GD), which plays an important role in quadruple systems’ construction. With application of Stern and Lenz’s result on one-factorization of graphs, by direct construction, it is given that the sufficient and necessary condition for the existence of the G-design with three groups
is that
.