There's an article published by NASA in which they discuss the practicality of using an evacuated blimp or airship on Mars. Their main points are that since the exterior pressure is so much lower, this could be constructed with a lattice of existing materials in a large sphere. They also predict that:
Through a more in-depth analysis of the vacuum airship model, it can be shown that the vacuum airship may theoretically carry more than twice as much payload as a modeled dirigible of the same size, a 40-meter radius, in the Martian atmosphere.
However it seems to me like the numbers don't add up...
If 1 cubic meter of atmosphere on Earth has a mass of about of about 1.225 kg/m^3 (asl) and the atmosphere on Mars (asl) is 0.6 percent of that then every cubic meter of vacuum can only displace 0.00735kg of Martian atmosphere. Now sure, Mars' gravity is also less but I'm still not quite sure how someone would construct a solid structure for less than 0.018kg which can contain a vacuum, even in mars' low pressure environment. Am I missing something? Where did my assumptions go wrong?