A construction method for complete sets of mutually orthogonal frequency squares
An \(n\times n\) matrix \(M\) over an \(m\)-set \(S\), \(n=\lambda m\), is called a frequency square of type \(F(n;\lambda)\) if every element of \(S\) occurs exactly \(\lambda\) times in each row and each column of \(M\), and two such matrices are called orthogonal if when one is superimposed on the other each element of \(S\times S\) appears \(\lambda^2\) times. A set of \({(n- 1)^2\over (m-1)}\) mutually orthogonal frequency squares (MOFS) of type \(F(n;\lambda)\) is called a complete set of type \(F(n;\lambda)\). Assuming the existence of affine designs with certain parameters and MOFS of suitable types the author generates MOFS of different types.
scientific article; zbMATH DE number 1498629