Combinatorial Arrays
 Balanced Arrays
Balanced Array is an (MxN)Array A with entries from a finite set S (S=s)
satisfying the following conditions:
(1) Let Y be an tvector of S^{t}. In any t rows of A, Y appears l(Y) times as colums,
(2) For any permutation P on coordinates of Y, l(Y)=l(P(Y))
 Orthogonal Arrays
If l(Y) is a constant number for any Y of S^{t}, then the array A is called an Orthogonal Array.
 Incomplete Orthogonal Arrays
Let E be a subset of S, If l(Y)=0 for any Y of E^{t} and l(Y) is a constsnt for
any Y of S^{t}  E^{t}, the array is called an Incomplete Orthogonal Array.
 Perpendicular Arrays
If l(Y) is a constant number for any Y consisting of t distinct elements of S
, otherwise l(Y)=0, then such an array A is said to be a Perpendicular Array.
Recent Publications
 A Note on Geometric Structure of Linear Ordered
Orthogonal Arrays and (T,M,S)nets of Low Strength (with Ying Miao)
Journal of Code , Designs and Cryptograph,26, pp.257263 (2002) (pdf)
 Balanced nested designs and balanced arrays (with S.Kageyama,S.Kuriki, Y.Miao and S.Shinohara)
, Discrete Mathematics, 259, pp.91119 (2002) (pdf)
 Balanced Arrays from Quadratic Functions ,Journal of Statistical Planning and Inference,
84 (2000), 285293 (pdf) (with Nobuko Miyamoto)
 Symmetric Sets of Curves and Combinatorial Arrays
Contemporary Mathematics, Vol. 225, (1999),pp. 225230
(with Satoshi Shinohara) (pdf)
 A Constructin of Combinatorial Arrays from Nonlinear functions
(pdf) , Utilitas Mathematica 52 (1997), pp.183192 (with Nobuko Miyamoto)

Cyclic Orthogonal and Balanced Arrays (pdf)
(with S. Kuriki) JSPI 56 (1996) 171180
 Balanced arrays with strength two and Nested (r,\lambda)Design(pdf)
(with S. Kuriki) Journal of Design Theory,Vol. 2, No. 6 (1994) 407414
 Orthogonal Arrays from Baer subplanes
Utilitus Mathematica 43(1993) pp.6570 (with S. Kamimura)
 Mutually balanced nested designs,
Discrete Mathematics, 97(1991) 167176 (with S. Kuriki)
 An Extension Method for Balanced Arrays
Communication in StatisticsTheory and Mathods, 20(3) 10731085
(with F.Yuan and M. Jimbo)
 A recursive construction of balanced arrays,
Utilitus Mathematica, 36 (with M. Jimbo and F. Yuan)
 On balanced complementation for regular twise balanced designs,
Discrete Mathematics 76 (with S. Kuriki and M. Jimbo)
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