Nearly Kirkman triple systems of order 18 (Q2768124)

A nearly Kirkman triple system of order \(6n\), or NKTS(\(6n\)), is a resolvable group divisible design with blocks of size 3 and \(3n\) groups of size 2. It was proved by various authors that an NKTS(\(6n\)) exists if and only if \(n \geq 3\). Thus, the smallest order for which an NKTS exists is 18. Prior to the present paper, there was, up to isomorphism, only one known example of an NKTS(18). The authors show that there are exactly 119 NKTS(18) of a particular type. The authors also construct several NKTS(18) not of that type, yielding a total of 135 presently known NKTS(18). However, the enumeration problem for general NKTS(18) remains open.