The Annals of Statistics

On the existence of saturated and nearly saturated asymmetrical orthogonal arrays

Rahul Mukerjee and C. F. Jeff Wu

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We develop a combinatorial condition necessary for the existence of a saturated asymmetrical orthogonal array of strength 2. This condition limits the choice of integral solutions to the system of equations in the Bose-Bush approach and can thus strengthen considerably the Bose-Bush approach as applied to a symmetrical part of such an array. As a consequence, several nonexistence results follow for saturated and nearly saturated orthogonal arrays of strength 2. One of these leads to a partial settlement of an issue left open in a paper by Wu, Zhang and Wang. Nonexistence of a class of saturated asymmetrical orthogonal arrays of strength 4 is briefly discussed.

Article information

Ann. Statist., Volume 23, Number 6 (1995), 2102-2115.

First available in Project Euclid: 15 October 2002

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Zentralblatt MATH identifier

Primary: 62K15: Factorial designs 05B15: Orthogonal arrays, Latin squares, Room squares

Bose-Bush bound Delsarte theory


Mukerjee, Rahul; Wu, C. F. Jeff. On the existence of saturated and nearly saturated asymmetrical orthogonal arrays. Ann. Statist. 23 (1995), no. 6, 2102--2115. doi:10.1214/aos/1034713649.

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