A Characterization of Designs Related to the Witt System S(5, 8, 24).
It is well known that given a Steiner triple system one can define a quasigroup operation upon its base set by assigning for all and , where is the third point in the block containing the pair . The same can be done for Mendelsohn triple systems, where is considered to be ordered. But this is not necessarily the case for directed triple systems. However there do exist directed triple systems, which induce a quasigroup under this operation and these are called Latin directed triple systems....