Some balanced repeated measurements designs

Abstract

Methods of constructing some Balanced Repeated Measurements Designs (RMD) are given. We consider a balanced $\mathrm{RMD}[\mathit{t}\mathrm{,}\mathit{t}\mathrm{(}\mathit{t}-1\mathrm{)}\mathrm{,}3]$ t being any positive integer (prime or non-prime). Using this method, an unsolved balanced $\mathrm{RMD}\mathrm{(}6\mathrm{,}30\mathrm{,}3\mathrm{)}$ is constructed. A method for constructing $\mathrm{RMD}[\mathit{t}\mathrm{,}\mathit{t}\mathrm{(}\mathit{t}-1\mathrm{)}\mathrm{,}\mathit{t}-1]$ , t being any odd integer, is given.