A small generating set for the 3‐BD closed set of block sizes ≥ 6

Let v, k be positive integers and k ≥ 3, then K_k = : {v: v ≥ k} is a 3‐BD closed set. Two finite generating sets of 3‐BD closed sets K₄ and K₅ are obtained by H. Hanani [5] and Qiurong Wu [12] respectively. In this article we show that if v ≥ 6, then v ∈ B₃(K,1), where K = {6,7,…,41,45,46,47,51,52,53,83,84}{22,26}; that is, we show that K is a generating set for K₆. Finally we show that v ∈ B₃(6,20) for all v ∈ K{35,39,40,45}. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 128–136, 2008