Constructions of \((q,k,1)\) difference families with \(q\) a prime power and \(k=4,5\)
The author gives new constructions for difference families with \(\lambda= 1\) and \(k= 4\) or 5 in (the additive groups of) finite fields. As an application, cyclic \((p,k,1)\)-difference families are exhibited in tabular form for \(k= 4\) and \(k= 5\) satisfying the necessary conditions (which are \(p\equiv 1\pmod {12}\) and \(p\equiv 1\pmod {20}\), respectively) in the range \(p< 10^ 4\); the author has also checked the applicability of his construction for \(k= 4\) up to \(10^ 6\). The construction uses Wilson's method of evenly distributed differences, see \textit{R. M. Wilson} [``Cyclotomy and difference families in elementary Abelian groups'', J. Number Theory 4, 17-47 (1972; Zbl 0259.05011)].
scientific article; zbMATH DE number 744007