  In this contribution, we outline the improvements on the strain h(t)
reconstruction in preparation for the observing run O4 of AdvancedVirgo+. These
improvements have the main goal to provide a h(t) with high precision and
reduce its uncertainties on this quantity to a few percent. First, we describe
how the reconstruction of the strain signal h(t) is performed in Virgo and its
link to the interferometer and its calibration. We highlight how we plan to
monitor the optical response of the interferometer and mirrors. We will
describe how we plan to correct the bias of the reconstructed h(t) strain. We
present the new online linear noise subtraction method, developed to
successfully tackle correlated noise witness channels that are also present in
h(t). We provide the status of the low-latency h(t) strain reconstruction,
which has the main goal to reduce the latency in pre-merger early warning
alerts.
