  The Robotic Optical Transient Search Experiment (ROTSE) seeks to measure
simultaneous and early afterglow optical emission from gamma-ray bursts (GRBs).
A search for optical counterparts to six GRBs with localization errors of 1
square degree or better produced no detections. The earliest limiting
sensitivity is m(ROTSE) > 13.1 at 10.85 seconds (5 second exposure) after the
gamma-ray rise, and the best limit is m(ROTSE) > 16.0 at 62 minutes (897 second
exposure). These are the most stringent limits obtained for GRB optical
counterpart brightness in the first hour after the burst. Consideration of the
gamma-ray fluence and peak flux for these bursts and for GRB990123 indicates
that there is not a strong positive correlation between optical flux and
gamma-ray emission.
