Large Set Of Kirkman Triple Systems With Order Q~n+2

The existence of Large sets of Kirkman Triple Systems (LKTS)is an old prob-lem in combinatorics.Known results are very limited, and a lot of them are based on the works of Denniston [2-5].The only known recursive constructions are an tripling construction by Denniston [5]and a product construction by Lei[10],both constructs an LKTS(ue) on the basis of an LKTS(e).In this thesis,we describe an construction of LKTS(qn+2)from LKTS(q+2), where q is a prime power of the form6t+1.We could construct previous unknown LKTS(e)by this result, the smallest among them have v=171.345,363.This thesis are divided into three sections. In section1,we give some basic definitions, review the results thus far, and state out main result;in section2,we describe the details of our construction;finally in section3,we give an example of out construction in the case q=13,n=2.