A S(3,{4,6}, 18) with a Subdesign S(3,4,8) Does Not Exist

摘要

For K subset of {1, 2, 3,...}, a S(t, K, v) design is a pair, (V, B), with vertical bar V vertical bar = v and B a set of subsets of V such that each t-subset of V is contained in a unique alpha is an element of B and vertical bar alpha vertical bar is an element of K for all alpha is an element of B. If U subset of V, vertical bar U vertical bar = u, A = (alpha is an element of B : alpha subset of U}, and (U, A) is a S(t, K, U) design, then we say (V, S) has a subdesign on U. We show that a S(3, 14, 6), 18) design with a subdesign S(3, 4, 8) does not exist.