Some results on two-level regular designs with multi block variables containing clear effects

Abstract

In this paper, the idea of clear effects is extended to the case of blocked regular $$2^{n{-}m}$$ designs with multi block variables. Some necessary and sufficient conditions on the existence of clear treatment main effects and clear treatment two-factor interactions (2fi’s) in $$2^{n{-}m}:2^l$$ designs with resolution III, IV $$^- $$ and IV are obtained, where the notation $$2^{n-m}:2^l$$ means that there are n treatment factors, m treatment defining words and l block variables. We discuss how to find $$2^{n-m}:2^l$$ designs with the maximum number of clear 2fi’s with resolution III, IV $$^-$$ or IV, and present some 16-, 32-, 64-run designs containing the maximum number of clear 2fi’s in tables.