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Friday 5:50–6:15 109 Oelman Hall
Non-embeddable Quasi-Derived Designs
Tariq Alraqad
Central Michigan University
Abstract
A derived design of a symmetric (v, k, λ)–design D, is a 2–(k, λ, λ − 1) design D ′ obtained from D
by removing a block B and replacing every other block A by A B. A 2-design that has parameters
of a derived design (equivalently k = λ + 1) is called a quasi-derived design. Moreover, it is said to be
embeddable if it is the derived design of a symmetric design.
The main result is a method of constructing a non-embeddable quasi-derived design from a quasiderived
design and an α-resolvable design. This method is a generalization of techniques used by van
Lint and Tonchev (1984,1993) and Kageyama and Miao (1996). As applications, several new families
of non-embeddable quasi-derived designs are constructed.
Friday 6:15–6:40 109 Oelman Hall
Classification of Orthogonal Arrays by Integer Programming
Dursun Bulutoglu
Air Force Institute of Technology
Abstract
In Bulutoglu and Margot (2007) the problem of classifying all isomorphism classes of OA(N, k, s, t)s
is shown to be equivalent to finding all isomorphism classes of non-negative integer solutions to a system
of linear equations under the symmetry group of the system of equations. In this paper a branchand-cut
algorithm developed by Margot (2002, 2003a, 2003b, 2005) for solving integer programming
problems with large symmetry groups is used to find all non-isomorphic OA(24, 7, 2, 2)s, OA(24, k, 2, 3)s
for 6 ≤ k ≤ 11, OA(32, k, 2, 3)s for 6 ≤ k ≤ 11, OA(40, k, 2, 3)s for 6 ≤ k ≤ 10, OA(48, k, 2, 3)s for 6 ≤
k ≤ 8, OA(56, k, 2, 3)s, OA(80, k, 2, 4)s, OA(112, k, 2, 4)s, for k = 6, 7, OA(64, k, 2, 4), OA(96, k, 2, 4)s
for k = 7, 8, and OA(144, k, 2, 4)s for k = 8, 9. Moreover further applications to classifying covering
arrays with the minimum number of runs and packing arrays with the maximum number of runs are
presented. I am going to talk about these new developments regarding orthogonal arrays.
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