  In this paper, combinatorial quantitative group testing (QGT) with noisy
measurements is studied. The goal of QGT is to detect defective items from a
data set of size $n$ with counting measurements, each of which counts the
number of defects in a selected pool of items. While most literatures consider
either probabilistic QGT with random noise or combinatorial QGT with noiseless
measurements, our focus is on the combinatorial QGT with noisy measurements
that might be adversarially perturbed by additive bounded noises. Since perfect
detection is impossible, a partial detection criterion is adopted. With the
adversarial noise being bounded by $d_n = \Theta(n^\delta)$ and the detection
criterion being to ensure no more than $k_n = \Theta(n^\kappa)$ errors can be
made, our goal is to characterize the fundamental limit on the number of
measurement, termed \emph{pooling complexity}, as well as provide explicit
construction of measurement plans with optimal pooling complexity and efficient
decoding algorithms. We first show that the fundamental limit is
$\frac{1}{1-2\delta}\frac{n}{\log n}$ to within a constant factor not depending
on $(n,\kappa,\delta)$ for the non-adaptive setting when $0<2\delta\leq \kappa
<1$, sharpening the previous result by Chen and Wang [1]. We also provide an
explicit construction of a non-adaptive deterministic measurement plan with
$\frac{1}{1-2\delta}\frac{n}{\log_{2} n}$ pooling complexity up to a constant
factor, matching the fundamental limit, with decoding complexity being
$o(n^{1+\rho})$ for all $\rho > 0$, nearly linear in $n$, the size of the data
set.
