  The task of non-adaptive group testing is to identify up to $d$ defective
items from $N$ items, where a test is positive if it contains at least one
defective item, and negative otherwise. If there are $t$ tests, they can be
represented as a $t \times N$ measurement matrix. We have answered the question
of whether there exists a scheme such that a larger measurement matrix, built
from a given $t\times N$ measurement matrix, can be used to identify up to $d$
defective items in time $O(t \log_2{N})$. In the meantime, a $t \times N$
nonrandom measurement matrix with $t = O \left(\frac{d^2
\log_2^2{N}}{(\log_2(d\log_2{N}) - \log_2{\log_2(d\log_2{N})})^2} \right)$ can
be obtained to identify up to $d$ defective items in time $\mathrm{poly}(t)$.
This is much better than the best well-known bound, $t = O \left( d^2
\log_2^2{N} \right)$. For the special case $d = 2$, there exists an efficient
nonrandom construction in which at most two defective items can be identified
in time $4\log_2^2{N}$ using $t = 4\log_2^2{N}$ tests. Numerical results show
that our proposed scheme is more practical than existing ones, and experimental
results confirm our theoretical analysis. In particular, up to $2^{7} = 128$
defective items can be identified in less than $16$s even for $N = 2^{100}$.
