On the maximum number of columns for supersaturated designs with s(max)is an element of{1,3,5
Por:
Morales, Luis B.
Publicada:
1 ene 2021
Resumen:
Cheng and Tang [Upper bounds on the number of columns in
supersaturated designs. Biometrika, 88 (2001), 1169-1174] provided upper
bounds on the maximum number of columns, denoted by B(n,t), that can be
accommodated in two-symbol supersaturated designs for a given number,
say n, of rows and a maximum correlation in absolute value, say t/n,
between any two columns. Recently, Morales et al [On the maximum
number of columns in supersaturated designs with s(max)=2, J. Combin.
Des., 27 (2019), 448-472] proved that B(n,2)=n+1 for n=14,18,22,30.
However, from the 35 lower bounds for B(n,t) provided by Cheng and Tang,
only 11 supersaturated designs are known to satisfy these bounds. In
this article, by performing a computer search, we show that B(9,1)=7,
B(13,1)=12, B(17,1)=15, B(21,1)=19, B(7,3)=15, B(9,3)=12,
B(11,3)=B(13,3)=15, B(11,5)=66, and B(15,3)=17. Likewise, our search
produces supersaturated designs that achieve these maximums. Each of
these exact values was previously unknown.
Filiaciones:
Morales, Luis B.:
IIMAS Sede Yucatán, UACTY, Universidad Nacional Autónoma de México, Mexico
Bronze
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