An Extended Class Of Resolvable, Incomplete Lattice Designs

Abstract

A method for synthesizing combinatorial structures which are members of an extended class of resolvable incomplete lattice designs is presented. Square and rectangular lattices both are realizable, yet designs in the extended class are not limited in number of treatments by the classically severe restriction $v=s^2$ or $v=s(s-1)$. Rather, the current restriction is the condition that there exist a finite closable set of $k$-permutations on the objects of some group or finite field, which is then used as the generating array for a $L(0,1)$ lattice design. A connection to Hadamard matrices $H(p,p)$ is considered.