2018/02/25 by Chariya Uiyyasathian, Uiyyasathian, Chariya, Nataphan Kitisin +1
Engineering · Decision Sciences · #graph theory and CDMA systems #Antenna Design and Optimization #Optimal Experimental Design Methods
paper · pdf · doi:10.48550/arxiv.1802.08968
A group divisible design GDD(m,n;λ1,λ2), is an ordered pair (V, \calB) where V is an (m+n)-set of symbols while \calB is a collection of 3-subsets (called blocks) of V satisfying the following properties: the (m+n)-set is divided into 2 groups of size m and of size n: each pair of symbols from the same group occurs in exactly λ1 blocks in \calB, and each pair of symbols from different groups occurs in exactly λ2 blocks in \calB. λ1 and λ2 are referred to as first index and second index, respectively. Here, we focus on an existence problem of GDDs when λ1=3 and λ2>3. We obtain the necessary conditions and prove that these conditions are sufficient for most of the cases.