  One of the most often implied benefits of high-dimensional (HD) quantum
systems is to lead to stronger forms of correlations, featuring increased
robustness to noise. Here, we experimentally demonstrate the $n$-setting linear
HD quantum steering criterion. We verify the large violation of the steering
inequalities without full-state tomography. The lower bound of the violation is
$2.24\pm0.01$ in 11 dimensions, exceeding the bound ($V<2$) of 2-setting
criteria. Hence, a higher strength of steering has been revealed. Moreover, we
demonstrate the method for enhancing the noise robustness without increasing
dimension, alternatively, by increasing measurement settings. Using the
entanglement in 11 dimensions, we experimentally retrieve steering nonlocality
with $63.4\pm1.4\%$ isotropic noise fraction, surpassing the $50\%$ limitation
of 2-setting criteria. Our work offers the potential for practical one-sided
device-independent quantum information processing that tolerates the noisy
environment, lossy detection, and transcends the present transmission distance
limitation.
