Some New Difference Sets

A difference set is a set D = {d 1 , d 2 , … , d k ] of k distinct residues modulo v such that each non-zero residue occurs the same number of times among the k(k — 1) differences d i — d j , i ≠ j. If λ is the number of times each difference occurs, then (1) When we wish to emphasize the particular values of v, k , and λ involved we will call such a set a (v, k , λ) difference set. Another (v, k , λ) difference set E = {e 1 , e 2 , … e k } is said to be equivalent to the original one if there exist a and t such that (t, v) = 1 and E = {a + td 1 , … , a + td k } . If t = 1 we will call the set E a slide of the set D . If D = E , then t is called a multiplier of D .