Enumeration of balanced ternary designs

AbstractA (V,B;ρ1,ρ2,R;K,Λ) balanced ternary design is a pair (V,B), where V is a V-set of points and B is a collection of B K-multisubsets of V called blocks, such that each point appears R times in the blocks and no block contains a point with multiplicity greater than two. Each point must appear in ρ1 blocks with multiplicity one and in ρ2 blocks with multiplicity two. Additionally, every pair of distinct points must appear exactly Λ times in the blocks of the design. A backtrack search algorithm with isomorph rejection is described and employed to enumerate the balanced ternary designs with V⩽10, B⩽30, and R⩽15 for all but 12 of the 155 possible design classes with these parameters