On orthogonal designs in order 48
The authors consider orthogonal designs of order 48 with three different entries. Here, an orthogonal design of order \(n\) is a \(n\times n\) square matrix with orthogonal rows. Moreover, the specified entries occur the same number of times in each row and in each column, where some of the entries may have a negative sign, and some may be zero. Different types of orthogonal designs are characterized by the number of replicates for the different entries. The authors claim that for order 48 and three different entries there are 3164 types, of which 3147 can be constructed by classical techniques. They propose two new methods of construction which can be used to obtain the remaining 17 types. No applications to statistics are indicated.
scientific article; zbMATH DE number 2137683