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](http://arxiv.org/abs/1101.5638). DOI:	[10.1142/S0218195913500076](http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1142%2FS0218195913500076&v=cbb3f697)