A deterministic counterexample for high dimensional $L^2{L}^{\mathrm{\infty }}$ Strichartz estimates for the Wave equation

In this note we discuss the question of homogeneous $L^2{L}^{\mathrm{\infty }}$ Strichartz estimates for the Wave equation in dimensions $n\ge 4$ raised by Fang and Wang and recently shown to fail by Guo, Li, Nakanishi and Yan using probability theory. We record a deterministic example for disproving this estimate.