A terrace for m is an arrangement (a1, a2, . . . , am) of the m elements of m such that the sets of differences ai+1 − ai and ai − ai+1 (i = 1, 2, . . . , m − 1) between them contain each element of m \ {0} exactly twice. For m odd, many procedures are available for constructing power-sequence terraces for m; each such terrace may be partitioned into segments, one of which contains merely the zero element of m, whereas each other segment is either (a) a sequence of successive powers of an element of m or (b) such a sequence multiplied throughout by a constant. We now adapt this idea by using power-sequences in n, where n is an odd prime power, to obtain terraces for m, where m = n − 2. We write each element from n so that they lie in the interval [0, n − 1] and then delete 0 and n − 1 so that they leave n − 2 elements that may be interpreted as the elements of n−2. A segment of one of the new terraces may be of type (a) or (b), incorporating successive powers of 2, with each entry evaluated modulo n. Our constructions provide n−2 terraces for all odd primes n satisfying 0 < n < 1,000 except for n = 127, 241, 257, 337, 431, 601, 631, 673, 683, 911, 937 and 953. We also provide n−2 terraces for n = 3r (r > 1) and for some values n = p2, where p is prime.

A terrace for $\mathbb{Z}_m$ is a particular type of sequence formed from the $m$ elements of $\mathbb{Z}_m$. For $m$ odd, many procedures are available for constructing power-sequence terraces for $\mathbb{Z}_m$; each terrace of this sort may be partitioned into segments, of which one contains merely the zero element of $\mathbb{Z}_m$, whereas every other segment is either a sequence of successive powers of an element of $\mathbb{Z}_m$ or such a sequence multiplied throughout by a constant. We now refine this idea to show that, for $m=n-1$, where $n$ is an odd prime power, there are many ways in which power-sequences in $\mathbb{Z}_n$ can be used to arrange the elements of $\mathbb{Z}_n\setminus\{0\}$ in a sequence of distinct entries $i$, $1\le i\le m$, usually in two or more segments, which becomes a terrace for $\mathbb{Z}_m$ when interpreted modulo $m$ instead of modulo $n$. Our constructions provide terraces for $\mathbb{Z}_{n-1}$ for all prime powers $n$ satisfying $0\ltn\lt300$ except for $n=125$, $127$ and $257$.