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A SERIES OF SEARCH DESIGNS FOR 2^{m} FACTORIAL DESIGNS

OF RESOLUTION V WHICH PERMIT SEARCH OF ONE OR TWO

UNKNOWN EXTRA THREE-FACTOR INTERACTIONS

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TERUHIRO SHIRAKURA^{1} AND SHINSEI TAZAWA^{2}

^{1} *Department of Mathematics, Kobe University, Nada-ku, Kobe 657, Japan*

^{2} *Department of Mathematics, Kinki University, Higashi-Osaka 577, Japan*
(Received January 11, 1990; revised July 30, 1990)

**Abstract.**
In the absence of four-factor and higher
order interactions, we present a series of search designs for
2^{m} factorials (*m* __>__ 6) which allow the search of at most *k*
(= 1,2) nonnegligible three-factor interactions, and the
estimation of them along with the general mean, main effects and
two-factor interactions. These designs are derived from balanced
arrays of strength 6. In particular, the nonisomorphic weighted
graphs with 4 vertices in which two distinct vertices are
assigned with integer weight *omega* (1 __<__ *omega* __<__ 3), are
useful in obtaining search designs for *k* = 2. Furthermore, it is
shown that a search design obtained for each *m* __>__ 6 is of the
minimum number of treatments among balanced arrays of strength 6.
By modifying the results for *m* __>__ 6, we also present a search
design for *m* =5 and *k* = 2.

*Key words and phrases*:
Search design, minimum treatment,
balanced array,
strength 6, weighted graph, isomorphic graph.

**Source**
( TeX ,
DVI ,
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