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Abstract The combinatorial object named t -spontaneous emission error design (t -SEED) was proposed by Beth et al. in 2003 in order to correct errors caused by quantum jumps. The newly rising category of t -SEEDs has been studied extensively in recent years. Especially, the maximal possible dimensions for 2-SEEDs with block size 3 were determined completely; lower bounds on 2-SEEDs were established by applying affine groups. In this paper we utilize the action of twisted affine groups on finite fields and obtain new lower bounds on the dimensions of 2- (q 2 , k ; m) SEEDs, some of which outperform the known ones. [ABSTRACT FROM AUTHOR]

Abstract: Sylvester’s problem, i.e., the problem of the existence of large sets of Kirkman triple systems (LKTSs), is one of the most challenging problems in combinatorial design theory. Most recursive constructions for LKTSs impose resolvable restrictions on the ingredient designs, making the recursions difficult to apply. In this note we provide necessary small designs by using spherical geometries and a direct construction. Finally, we prove the existence of LKTS for all positive integers . A new result on overlarge sets of Kirkman triple systems is also produced. [Copyright &y& Elsevier]

Abstract: An LRMTS is a large set consisting of pairwise disjoint resolvable Mendelsohn triple systems defined over the same -element set. In this paper a new product construction for LRMTS is displayed by using generalized LR-designs. As well, several new existence families of LRMTS are constructed via 3-wise balanced designs. Finally the existence result of LRMTS is expanded by combining all the known constructions. [Copyright &y& Elsevier]

Abstract: Impulse radio sequences (IRSs) were introduced by Chu and Colbourn to study sequence or signal design for ultrawideband radio with unmodulated time-hopping. The central researches on IRSs lie in the determination of the value , i.e., the largest possible number of sequences in an -IRS. When , Chang and Wang have determined the value of . As far as the authors know, there has been no study on the case of . So we in this paper focus on this case with . We will determine the exact value of for any positive integers and . We also calculate the exact value of for and . [Copyright &y& Elsevier]

Abstract: The problem of the existence of large sets of Kirkman triple systems (LKTS) is one of the most celebrated open problems in design theory. Only a few sparsely distributed infinite classes have been determined, although LKTS have been investigated by many authors. The purpose of this paper is to survey constructions and results on LKTS and related designs. A systematic account of this work is provided. Most of the known constructions are unified and generalized; the approaches to LKTS are enriched; a couple of new constructions for related designs are also displayed. In particular, a new existence class of LKTS is demonstrated and some new results of overlarge sets of Kirkman triple systems are also produced. [Copyright &y& Elsevier]

Abstract: The concept of good large set of Steiner triple systems (or GLS in short) was introduced by Lu in his paper “on large sets of disjoint Steiner triple systems”, [J. Lu, On large sets of disjoint Steiner triple systems, I–III, J. Combin. Theory (A) 34 (1983) 140-182]. In this paper a doubling construction for GLSs is displayed and some existence results are obtained. [Copyright &y& Elsevier]

Abstract: Let X be a ( 2 n + 4 )‐set and G be a partition of X into n groups of size 2 and one group G0 of size 4. A large‐set‐plus denoted by LS + ( 2 n 4 1 ) is a partition of all G‐transverse triples of X into 2 ( n − 1 ) block sets of 3‐GDD(2n41)s with group set G, and two block sets of 3‐GDD(2n)s with group set G ∖ { G 0 }. In this paper, we study the existence problem of LS + ( 2 n 4 1 )s and give a nearly complete solution. [ABSTRACT FROM AUTHOR]

Abstract: The necessary and sufficient conditions for the existence of a -GDD of type have been established by Colbourn et al. In this paper, the existence of a -GDD of type for any is investigated. Finally, its existence spectrum is completely determined. [Copyright &y& Elsevier]

Abstract: An idempotent quasigroup of order is called resolvable (denoted by RIQ) if the set of non-idempotent 3-vectors can be partitioned into disjoint transversals. An overlarge set of idempotent quasigroups of order , briefly by OLIQ, is a collection of IQs, with all the non-idempotent 3-vectors partitioning all those on a -set. An OLRIQ is an OLIQ with each member IQ being resolvable. In this paper, it is established that there exists an OLRIQ for any positive integer , except for , and except possibly for . An OLIQ is another type of restricted OLIQ in which each member IQ has an idempotent orthogonal mate. It is shown that an OLIQ exists for any positive integer , except for , and except possibly for . [Copyright &y& Elsevier]