Super-simple designs with v≤32

A t-(v, k, lambda) 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 lambda blocks. Let p(D) = max (1 less than or equal to i < j <less than or equal to> b) \B(i)boolean ANDB(j)\. Let p* = p*(t, v; k, lambda) = mine(D) p(D), where D is a t-(v, k, lambda) design. A super-simple t-(v, k, lambda) design D is one with p(D) = p*. In this paper we survey known results and present some new super-simple 2-(v,4,lambda) designs for v less than or equal to 32. (C) 2001 Elsevier Science B.V. All rights reserved.