  It is known that all resolution IV regular $2^{n-m}$ designs of run size
$N=2^{n-m}$ where $5N/16<n<N/2$ must be projections of the maximal even design
with $N/2$ factors and, therefore, are even designs. This paper derives a
general and explicit relationship between the wordlength pattern of any even
$2^{n-m}$ design and that of its complement in the maximal even design. Using
these identities, we identify some (weak) minimum aberration $2^{n-m}$ designs
of resolution IV and the structures of their complementary designs. Based on
these results, several families of minimum aberration $2^{n-m}$ designs of
resolution IV are constructed.
