What is the computational complexity of solving a linear program with $m$ constraints in $n$ variables?
The best possible (I believe) is by Michael Cohen, Yin Tat Lee, and Zhao Song: Solving linear program in the current matrix multiplication time. https://arxiv.org/abs/1810.07896 (STOC 2019) Hope this helps.
Brand's 2020 result derandomized the Cohen, Lee and Song result. Here is the link https://arxiv.org/pdf/1910.11957.pdf