Two resolutions of the same 3-design are said to be orthogonal when each parallel class of one resolution has at most one block in common with each parallel class of the other resolution. If a Steiner quadruple system has two mutually orthogonal resolutions, the design is called doubly resolvable and denoted by DRSQS. In this paper, we define almost doubly resolvable candelabra quadruple system and then to get a recursive construction of DRSQS, i.e., for \(n\ge 16\), if there is a DRSQS(n), then there exists a DRSQS\((14n-12)\) and a DRSQS\((16n-12)\).

中文翻译：

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双可解析斯坦纳四元系统的递归构造

当一个分辨率的每个并行类与另一分辨率的每个并行类至多有一个公共块时，同一 3 设计的两个分辨率被认为是正交的。如果斯坦纳四重系统具有两个相互正交的分辨率，则该设计称为双可解析并用 DRSQS 表示。本文定义了几乎双可解的烛台四重系统，然后得到了DRSQS的递归构造，即对于\(n\ge 16\)，如果存在一个DRSQS( n )，则存在一个DRSQS \( (14n-12)\)和 DRSQS \((16n-12)\)。