Existence results for generalized balanced tournament designs with block size 3 (Q1209222)

A generalized balanced tournament design, \(\text{GBTD} (n,k)\) defined on a \(kn\)-set \(V\), is an arrangement of the blocks of a \((kn,k,k-1)\)-BIBD defined on \(V\) into an \(n \times (kn-1)\) array such that (1) every element of \(V\) is contained in precisely one cell of each column, and (2) every element of \(V\) is contained in at most \(k\) cells of each row. By utilizing direct and recursive constructions, the author completely determines the spectrum of \(\text{GBTD} (n,3)\). It is also proved that all positive integers \(n \geq 4\) belong to the spectrum of a factored \(\text{GBTD} (n,3)\), with one possible exception when \(n=23\).