The lattice constant 'a' depends on inverse gauge coupling \(\beta\), since beta is temperature dependent and with increase in temperature the lattice spacing decreases. This can be found from experiments and is explained at Appendix B of https://arxiv.org/pdf/1111.1710.pdf, where the quantity in left hand side of equation B1, is a/r1 which is calculated on lattice (since it is dimensionless), and in right hand side, we are doing curve fitting of function which depends on \(\beta\)(where the function is inspired from Renormalisation Group equation).