Before revision:  We also show that a 2^{o(1/\varepsilon^{d-1})} \text{poly (n) algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH).
After revision:  We also show that a 2^{o(1/\varepsilon^{d-1})} \mathrm{poly (n) algorithm would violate the Gap-Exponential Time Hypothesis (Gap-ETH).