A new infinite class of S(3, {4, 5, 7}, v)



A t-wise balanced design (atBD) of order v and block sizes from K, denoted by S(t, K, v), is a pair (X, ), where X is a v-element set and ℬ is a set of subsets of X, called blocks, with the property that |B|∈K for any B∈ℬ and every t-element subset of X is contained in a unique block. In this article, we shall show that there is an S(3, {4, 5, 7}, v) for any positive integer v7(mod12) with v19. Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 20:68–80, 2012