Designs with mutually orthogonal resolutions (Q1088989)

A combinatorial design D with replication number r is said to be resolvable if the blocks of D can be partitioned into classes \(R_ 1,R_ 2,...,R_ r\) such that each element of D is contained in precisely one block of each class. Two resolutions R and R' of D are called orthogonal if \(| R_ i\cap R_ j'| \leq 1\) for all \(R_ i\in R\), \(R_ j'\in R'\). A set \(Q=\{R^ 1,R^ 2,...,R^ t\}\) of t resolutions of D is called a set of mutually orthogonal resolutions (MORs) if the resolutions of Q are pairwise orthogonal. The authors construct designs with sets of t MORs for several sequences of t. Furthermore, for given designs they determine upper bounds for t.