The lower bound (initially provided by Khandawit and Sriwasdi) was improved in 2009 by Dimitrios Pagonakis. The bound was improved from 0.227498 to 0.231999.
Tirasan Khandhawit, Dimitrios Pagonakis, Sira Sriswasdi. Lower Bound for Convex Hull Area and Universal Cover Problems. Int.J.Comput.Geom.Appl. 23 (2013) 197-212. arXiv:1101.5638. DOI: 10.1142/S0218195913500076
