Further results on nearly Kirkman triple systems with subsystems
The known existence results for nearly Kirkman triple systems (NKTSs) with subsystems are improved upon. For an NKTS of order \(u\) to have an NKTS of order \(v\) as a subsystem, basic necessary conditions are that \(v\equiv u\equiv 0\pmod 6\), \(u\geq 3v\) and \(v\geq 18\). These conditions are shown to be sufficient whenever \(18\leq v\leq 72\), and also when \(u\geq 3.5v\) and \(v\geq 78\). Many new NKTSs with subsystems, and some new 4-GDDs, found by computer-assisted direct construction, are also presented.
scientific article; zbMATH DE number 1974986