An improved product construction for large sets of Kirkman triple systems

作者：Zhang S^*; Zhu L

来源：Discrete Mathematics, 2003, 260(1-3): 307-313.

DOI：10.1016/S0012-365X(02)00766-5

• LR-design
• large set of Kirkman triple systems
• transitive resolvable idempotent symmetric
• quasigroup

It has been shown by Lei, in his recent paper, that there exists a large set of Kirkman triple systems of order uv (LKTS(uv)) if there exist an LKTS(v), a TKTS(v) and an LR(u), where a TKTS(v) is a transitive Kirkman triple system of order u, and an LR(u) is a new kind of design introduced by Lei. In this paper, we improve this product construction by removing the condition "there exists a TKTS(v)". Our main idea is to use transitive resolvable idempotent symmetric quasigroups instead of TKTS. As an application, we can combine the known results on LKTS and LR-designs to obtain the existence of an LKTS(3(n)m(2 . 13(n1) + 1)...(2 . 13(nt) + 1)) for n greater than or equal to 1, m is an element of {1, 5, 11, 17, 25, 35, 43, 67, 91, 123} boolean OR {2(2r+1)25(8)+1 : r greater than or equal to 0, s greater than or equal to 0}, t greater than or equal to 0 and n(i) greater than or equal to 1 (i = 1,..., t).

• 出版日期2003-1-6
• 单位宿州学院; 苏州大学