A COMPLETION OF LU DETERMINATION OF THE SPECTRUM FOR LARGE SETS OF DISJOINT STEINER TRIPLE-SYSTEMS

Lu [6, 7, 8] proved that large sets of disjoint S(2, 3, v) exist for all v ≡ 1 or 3 (mod 6), v ≠ 7. However, due to the death of the author, [8] remained unfinished and crucial parts of the proof for six values were lost. As Lu's result can be used in many other combinatorial problems, the fact that nobody actually could provide a construction for these values was very annoying. It is the purpose of this paper to complete the proof for these six values. Our method is different from the procedure suggested in [8], but uses the same combinatorial structures, namely LD(n). Our new construction for LD(n) also allows us to substantially shorten Lu's proof. © 1991.