About the number of maximal subsystems in S(2,4,v)

Abstract

It's of great interest, to find systems S(2,4,v) with subsystems S(2,4,r=1/3(v-1)) – known as maximal subsystems. Up to now there exist only a few results – mainly due to Resmini and Shen. In this paper we prove a new partial result: Exactly for all v∊{121,40}+108N there exists a system S(2,4,v) with exactly two, but also a system with exactly four maximal subsystems.