High-convergence implosion experiments have been performed on the Omega laser facility [T.R. Boehly, Opt. Commun. 133, 495 (1997)]] using cylindrical gold hohlraums with 40 drive beams arranged into multiple cones. These experiments make use of improved hohlraum radiation symmetry conditions [T.J. Murphy, Phys. Rev. Lett. 81, 108 (1998)]] to demonstrate near predicted primary (2.45 MeV) neutron production from single-shell implosions with measured deuterium fuel convergence ratios exceeding 20 at an ignition-relevant hohlraum case-to-capsule ratio approximately 3.