| Abstract: | In this article, it is shown that the necessary condition for the existence of a holey perfect Mendelsohn design (HPMD) with block size 5 and type hn, namely, n ≥ 5 and n(n - 1)hn ≡ 0 (mod 5), is also sufficient, except possibly for a few cases. The results of this article guarantee the analogous existence results for group divisible designs (GDDs) of group-type hn with block size k = 5 and having index λ = 4. Moreover, some more conclusive results for the existence of (v, 5, 1)-perfect Mendelsohn designs (PMDs) are also mentioned. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 257–273, 1997 |
