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\noindent Statistica Sinica {\bf 15}(2005), 731-749

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\centerline{\large\bf ORTHOGONAL  ARRAYS OF STRENGTH THREE AND}
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\centerline{\large\bf  SIZE $\mbf {2^r}$}
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\author{Chung-yi Suen}
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\centerline{\it Cleveland State University}
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\begin{quotation}
\noindent {\it Abstract:}
 The paper attempts to construct all orthogonal arrays of strength three and size $2^r$.
 Methods for constructing asymmetric orthogonal arrays are developed. By using the theories
 of finite field and finite projective geometry, several new series of orthogonal arrays are obtained.
 Many other orthogonal arrays are derived from the new series. A list of parameters of known symmetric
 and asymmetric    orthogonal arrays of strength three and size $2^r$
 ($r \le 8$) is provided. Parameters of unknown orthogonal arrays which satisfy Rao's bound are also
 included in the list.\par
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\noindent {\it Key words and phrases:}
Finite field, finite projective geometry, geometric, orthogonal array, oval, ovaloid, resolution IV plan, tight.\par
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