Search Design of Resolution III.3 for $3^4$Factorial

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). A series of resolution III.2 search design for $3^n, n=4, 5, 6$ are presented in Um (1988). In this paper a resoultion III.3 search design for $3^4$ is presented.