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Fig. 2.10
Construct a
00000
01010
00110
00111
0 1101
00001
11110
1 0100
11000
11001
1 0011
11111
CA
(
12
,
2
5
,
3
)
from a
DCA
(
4
,
3
;
2
)
R
(
i
,
u
,
e
)
=
(
d
i
1
+
u
), (
d
i
2
+
u
), (
d
i
3
+
u
+
e
), (
d
i
4
+
u
+
e
),
e
,
G
. These
nv
2
nv
2
v
5
where
u
,
e
∈
row vectors form a CA
(
,
,
3
)
.
2
5
Example 2.7
From the DCA
)
in Fig.
2.10
using this method. Each row vector in the DCA would produce four row
vectors in the CA since there are four value combinations of
u
and
e
.
(
4
,
3
;
2
)
in Fig.
2.8
, we can construct a CA
(
12
,
,
3
There are also constructive methods to produce CAs of higher strength from
DCAs. For example, CAs of strength 5 can be built with the methods in [
7
].
References
1. Chateauneuf, M., Kreher, D.: On the state of strength-three covering arrays. J. Comb. Des.
10
(4), 217-238 (2002)
2. Colbourn, C.J.: Combinatorial aspects of covering arrays. Le Matematiche (Catania)
58
, 121-
167 (2004)
3. Colbourn, C.J., Dinitz, J.H. (eds.): Handbook of Combinatorial Designs, 2nd edn. Chapman
& Hall / CRC, Boca Raton (2006)
4. Colbourn, C.J., Martirosyan, S.S., Mullen, G.L., Shasha, D., Sherwood, G.B., Yucas, J.L.:
Products of mixed covering arrays of strength two. J. Comb. Des.
14
(2), 124-138 (2006)
5. Hall Jr, M.: Combinatorial Theory, 2nd edn. Wiley, New York (1998)
6. Ji, L., Yin, J.: Constructions of new orthogonal arrays and covering arrays of strength three. J.
Comb. Theory Ser. A
117
, 236-247 (2010)
7. Ji, L., Li, Y., Yin, J.: Constructions of covering arrays of strength five. Des. Codes Cryptogr.
62
(2), 199-208 (2012)
8. Stevens, B., Mendelsohn, E.: New recursive methods for transversal covers. J. Comb. Des.
7
(3), 185-203 (1999)
9. Yan, J., Zhang, J.: A backtracking search tool for constructing combinatorial test suites. J. Syst.
Softw.
81
(10), 1681-1693 (2008)
10. Yin, J.: Constructions of difference covering arrays. J. Comb. Theory Ser. A
104
(2), 327-339
(2003)
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