Near-complete external difference families |
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Authors: | James A Davis Sophie Huczynska Gary L Mullen |
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Institution: | 1.Department of Mathematics and Computer Science,University of Richmond,Richmond,USA;2.School of Mathematics and Statistics,University of St. Andrews,St. Andrews,Scotland, UK;3.Department of Mathematics,Pennsylvania State University,University Park,USA |
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Abstract: | We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings. |
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