Abstract. The existence of large sets of 5-ð14; 6; 3Þ designs is in doubt. There are five simple 5-ð14; 6; 6Þ designs known in the literature. In this note, by the use of a computer program, we show that all of these designs are indecomposable and therefore they do not lead to large sets of 5-ð14; 6; 3Þ designs. Moreover, they provide the first counterexamples for a conjecture on disjoint t-designs which states that if there exists a t-ðv; k; lÞ design ðX; DÞ with minimum possible value of l, then there must be a t-ðv; k; lÞ design ðX; D 0 Þ such that D \ D 0 ¼ 1