Some Zn+2Zn+2 terraces from ZnZn power-sequences, n being an odd prime

A terrace for ZmZm is an arrangement (a1,a2,…,am)(a1,a2,…,am) of the m   elements of ZmZm such that the sets of differences ai+1-aiai+1-ai and ai-ai+1ai-ai+1(i=1,2,…,m-1)(i=1,2,…,m-1) between them contain each element of Zm⧹{0}Zm⧹{0} exactly twice. For m   odd, many procedures are available for constructing power-sequence terraces for ZmZm; each terrace of this sort may be partitioned into segments one of which contains merely the zero element of ZmZm, whereas each other segment is either (a) a sequence of successive powers of an element of ZmZm or (b) such a sequence multiplied throughout by a constant. We now extend this idea by using power-sequences in ZnZn, where n   is an odd prime, to obtain terraces for ZmZm where m=n+2m=n+2. Our technique needs each of the n-1n-1 elements from Zn⧹{0}Zn⧹{0} to be written so as to lie in the interval (0,n)(0,n) and for three further elements 0, n   and n+1n+1 then to be introduced. A segment of one of the new terraces may contain just a single element from the set S0={0,n,n+1}S0={0,n,n+1} or it may be of type (a) or (b) with m=nm=n and containing successive powers of 2, each evaluated modulo n  . Also, a segment based on successive powers of 2 may be broken in one, two or three places by putting a different element from S0S0 in each break. We provide Zn+2Zn+2 terraces for all odd primes n   satisfying 0