The existence of partitioned balanced tournament designs

Abstract

E. R. Lamken prove in [5] that there exists a partitioned balanced tournament design of side $n$, PBTD($n$), for $n$ a positive integer, $n\ge 5$, except possibly for $n\in \{9,11,15\}$. In this article, we show the existence of PBTD($n$) for $n\in \{9,11,15\}$. As a consequence, the existence of PBTD($n$) has been completely determined.