Search Design of Resolution III.2 for $3^n,n=4,5,6^+$

The basic conditions for a parallel-flats fraction to be a search design of Resolution III.2 have been developed in Um (1980, 1981, 1983, 1984). In this paper, a series of resolution III.2 search designs for $3^n, n=4, 5, 6$, are presented.