The spectrum for large sets of disjoint mendelsohn triple systems with any index

Abstract

The spectrum for LMTS(v, 1) has been obtained by Kang and Lei (Bulletin of the ICA, 1993). In this article, firstly, we give the spectrum for LMTS(v,3). Furthermore, by the existence of LMTS(v, 1) and LMTS(v, 3), the spectrum for LMTS(v, A) is completed, that is

Completing the spectrum for LGDD (mv)

“…By Lemma 1, there exist an S (3,6,26) and an S (3,8,50). By Corollary, there exist F (3, 3, 5{6}), F (3, 3, 6{6}), F (3, 3, 7{6}), and F (3, 3, 8{6}).…”

Further results on large set of disjoint pure Mendelsohn triple systems

“…It is well known [2,7,9] that Recently, in order to construct``Generalized Steiner Systems''Ða type of new designs which are equivalent to maximum constant weight codes, Kevin Phelps and Carol Yin posed the open problem in 10 of ®nding large sets of disjoint pure MTSv. Bennett, Kang, Zhang, and author have given some preliminary results (see [3]).…”

Large Sets and Overlarge Sets of Triangle-Decomposition

“…F 49 : t = 24, primitive polynomial g 2 = 4 + g, (α 0 , β 0 , r 0 ) = (29, 33, 15), (α 1 , · · · , α 23 ) = (0, 2, 3,5,7,8,11,13,15,32,23,28,26,30,31,19,20,27,17,38,22,25,41).…”

“…F 25 : t = 12, primitive polynomial g 2 = 2 + 2g, (α 0 , β 0 , r 0 ) = (18,22,5), (α 1 , · · · , α 11 ) = (0, 2, 3, 10,7,17,8,13,11,9,5). F 49 : t = 24, primitive polynomial g 2 = 4 + g, (α 0 , β 0 , r 0 ) = (29, 33, 15), (α 1 , · · · , α 23 ) = (0, 2, 3,5,7,8,11,13,15,32,23,28,26,30,31,19,20,27,17,38,22,25,41).…”