  Supersaturated design (SSD) has received much recent interest because of its
potential in factor screening experiments. In this paper, we provide equivalent
conditions for two columns to be fully aliased and consequently propose methods
for constructing $E(f_{\mathrm{NOD}})$- and $\chi^2$-optimal mixed-level SSDs
without fully aliased columns, via equidistant designs and difference matrices.
The methods can be easily performed and many new optimal mixed-level SSDs have
been obtained. Furthermore, it is proved that the nonorthogonality between
columns of the resulting design is well controlled by the source designs. A
rather complete list of newly generated optimal mixed-level SSDs are tabulated
for practical use.
