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Starter-adder methods in the construction of Howell designs

Published online by Cambridge University Press:  09 April 2009

B. A. Anderson  and
K. B. Gross
B. A. Anderson
Affiliation:
Arizona State University, Tempe, Arizona 85281.
K. B. Gross
Affiliation:
Michigan State University, East Lansing, Michigan 48824.
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Abstract

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The powerful starter-adder theorems for constructing Howell Designs are improved and consequently many types of Howell Designs that previously could only be constructed by multiplicative techniques are shown amenable to a modified starter-adder method. The existence question for Howell Designs of many new types H(s, 2n) is settled affirmatively. For prime powers pn, p ≧ 7, we reduce the entire existence question for designs of type H*(pn, 2r), pn + 1 ≦ 2r ≦ 2pn to the corresponding question for designs of type H*(p, 2m), p + 1 ≦ 2m≦2p. If these designs exist, s has no prime divisors ≤ 7 and t odd is “close” to 1, a design H * (s, s + t) is shown to exist.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 3 , November 1977 , pp. 375 - 384
Copyright
Copyright © Australian Mathematical Society 1977

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