Abstract
A Mendelsohn triple system MTS(v,b) is a collection of b cyclic triples (blocks) on a set of v points. It is j-balanced for j=1,2,3 when any two points, ordered pairs, or cyclic triples (resp.) are contained in the same or almost the same number of blocks (difference at most one). A (2,3)-balanced Mendelsohn triple system is an MTS(v,b) that is both 2-balanced and 3-balanced. Employing large sets of Mendelsohn triple systems and partitionable Mendelsohn candelabra systems, we completely determine the spectrum for which a 2-balanced Mendelsohn triple system exists. Meanwhile, we determine the existence spectrum for a (2,3)-balanced Mendelsohn triple system.
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