The existence of (M, B)-optimal designs for block size three is completely settled. Such a design is a collection of b triples on v elements so that for every two elements the numbers of triples containing them differ by at most one, and for every two pairs of elements the numbers of triples containing them also differ by at most one.
['Charles J. Colbourn', 'Alan C. H. Ling']
(M.S)-optimal designs with block size three