Existence of large sets of coverings with block size 3

Two types of large sets of coverings were introduced by T. Etzion (J Combin Designs, 2(1994), 359–374). What is maximum number (denoted by λ( n,k )) of disjoint optimal ( n,k,k  − 1) coverings? What is the minimum number (denoted by µ( n,k )) of disjoint optimal ( n,k,k  − 1) coverings for which the union covers the space? For k  = 3, the numbers µ( n,k ) have been determined with an unsolved order n  = 17, and the numbers λ( n,k ) have also been determined with an unsolved infinite class n  ≡ 5 (mod 6). The unsolved numbers λ( n ,3) and µ(17,3) will be completed in this note. This solution is based on the existence of a class of partitionable candelabra systems. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 400–405, 2006