In this thesis a powerful algorithm is developed for finding cyclic Steiner systems. A cyclic Steiner system with parameters S(t,k,v) is a pair ( V,B), where B is a collection of subsets all of size k (called blocks) and V is a t; element set of points, such that each t-subset of V is contained in precisely one block of B. A Steiner system is called cyclic if it has an automorphism carrying the points in a v-cycle. The results obtained so far with this algorithm are given in Table VII of chapter 5. Among the values reported there, are the number of distinct cyclic solutions to S(2,3,55), S(2,3,57), S(2,3,61) and S(2,3,63) which are 121,098,240, 84,672,512, 2,542,203,904 and 1,782,918,144 respectively. These values were apparently unknown previous to this work.

Library of Congress Subject Headings

Steiner systems--Data processing; Block designs--Data processing

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Computer Science (GCCIS)


Kreher, Donald


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