Construction of orthogonal starters and corollaries

A method is proposed for constructing a system of (v–1)/2 pairwise disjoint orthogonal starters of order v for v6k+17 (mod 12)pn²+n+1/t such that the number 3 is one of the primitive roots of the Galois field of prime order p (k is prime, k 2, and n and t are positive integers). The starters occurring in this system satisfy certain additional conditions. The construction of a series of combinatorial structures, including some not previously known, is a consequence of this result.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 5, pp. 654–662, May, 1992.