Near-Cyclic Representations for Some Resolution VI Fractional Factorial Plans

Abstract

Draper and Mitchell (1968) gave the complete set of even 512-run designs of resolution $\geqq 6$ and the complete set of 256-run designs of resolution $\geqq 5$. The authors showed that each of these designs can be obtained from one or other of five Reference Designs, all of resolution 6. The present note gives near-cyclic representations of the complete sets of interactions in the identity relationships of the Reference Designs. Some of these sets are shown to be related to certain incomplete block designs, including a resolvable balanced incomplete block design of a type that seems to have eluded attention hitherto.