  Flux tube spectra are expected to have full towers of levels due to the
quantization of the string vibrations. We study a spectrum of flux tubes with
static quark and antiquark sources with pure gauge $SU(3)$ lattice QCD in 3+1
dimensions up to a significant number of excitations. To go high in the
spectrum, we specialize in the most symmetric case $\Sigma_g^+$, use a large
set of operators, solve the generalized eigenvalue and compare different
lattice QCD gauge actions and anisotropies.
