| Abstract: | Jacobson and Matthews introduced the most hopeful method known for efficiently generating uniformly distributed random Latin squares. Cameron conjectures that the same Markov chain will also generate all of the other generalized 2‐designs with block size 3 uniformly at random. For a generalization of Latin squares, we give an affirmative result for any admissible parameter values. We also give the first insight and analysis into a generalization of the 1‐factorization of the complete graph by giving an affirmative result for some admissible parameter values. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 368–380, 2012 |
