On The Construction of Some L 2 Designs

Abstract

Abstract

A solution of L₂ design with the parameters $v=k^2,b=2k\left(k-1\right),r=2\left(k-1\right),k=k,{\lambda }_1=0,\hspace{0.17em}{\lambda }_2=2$ has been obtained when the symbols within the sets of the irreducible BIB design having the parameters $v*=k=b*,r*=k-1=k*,\lambda *=k-2$ can be arranged in cycles so that the PD-values for any ordered pair of symbols over all these cycles do not represent a PD-set 'more frequently' than its cardinality. A solution of the unsolved L₂ design with the parameters $v=36,b=60,r=10,k=6,{\lambda }_1=0,{\lambda }_2=2$ as reported by Chang and Liu (1964) has been obtained as a particular case.