Near generalized balanced tournament designs with block sizes 4 and 5 (Q1044268)

A near generalized balanced tournament design, NGBTD\((k,m)\) is a \((km+1,k,k-1)\) BIBD whose blocks can be put into a \(m \times (km+1)\) array so that (1) the blocks in each column form a partial parallel class missing one point of the BIBD, and (2) each of the \(km+1\) points appears in \(k\) blocks in each row. The authors prove that for \(k=4\) and \(5\), a NGBTD\((k,m)\) exists for all positive integers \(m\), except possibly for \(k=5\) and \(v \in \{15,32,40,45\}\). A number of small designs are constructed directly, using the starter-adder technique; larger designs are constructed recursively, frequently by using frame generalized doubly resolvable packings (FGDRPs).