Super-simple designs with v⩽32

Abstract

Abstract A t-(v,k,λ) design D=(X, B ) is a collection B ={B 1 ,B 2 ,…,B b } of k-subsets (called blocks) of a v-set X (with elements called points) such that every t-subset of X is contained in precisely λ blocks. Let p D = max 1⩽i |B i ∩B j | . Let p ∗ =p ∗ (t,v,k,λ)= min D p D , where D is a t-(v,k,λ) design. A super-simple t-(v,k,λ) design D is one with p D =p ∗ . In this paper we survey known results and present some new super-simple 2-(v,4,λ) designs for v⩽32.