  We present an exact enumeration algorithm for identifying the {\it native}
configuration - a maximally compact self avoiding walk configuration that is
also the minimum energy configuration for a given set of contact-energy
schemes; the process is implicitly sequence-dependent. In particular, we show
that the 25-step native configuration on a diamond lattice consists of two
sheet-like structures and is the same for all the contact-energy schemes,
${(-1,0,0);(-7,-3,0); (-7,-3,-1); (-7,-3,1)}$; on a square lattice also, the
24-step native configuration is independent of the energy schemes considered.
However, the designing sequence for the diamond lattice walk depends on the
energy schemes used whereas that for the square lattice walk does not. We have
calculated the temperature-dependent specific heat for these designed sequences
and the four energy schemes using the exact density of states. These data show
that the energy scheme $(-7,-3,-1)$ is preferable to the other three for both
diamond and square lattice because the associated sequences give rise to a
sharp low-temperature peak. We have also presented data for shorter (23-, 21-
and 17-step) walks on a diamond lattice to show that this algorithm helps
identify a unique minimum energy configuration by suitably taking care of the
ground-state degeneracy. Interestingly, all these shorter target configurations
also show sheet-like secondary structures.
