Halogen Oxyacid Trend (acid strength)
In the determination of the $\mathrm{pK_a}$ values of really strong acids, water as a medium is irrelevant at a certain point. 

Ivo Leito and coworkers have examined the acidity of various compounds in 1,2-dichloroethane (DCE).

In this medium the $\mathrm{pK_a}$ values for $\ce{HCl}$, $\ce{HNO3}$, $\ce{HBr}$, $\ce{HI}$, $\ce{HBF4}$, an $\ce{HClO4}$ have been determined as -0.4, -1.7, -4.9, -7.7, -10.3 and -13.0.



In this survey, 1,1,2,3,3-pentacyanopropene (1), was found to be even more acidic with a $\mathrm{pK_a}$ of -15.0!


EDIT 
It is important to note that these values are likely to be correct in their relative order. But the values are based on picric acid, for which the $\mathrm{pK_a}$ was arbitrarily set to zero. This initially escaped my attention! 

Thanks to Martin for pointing out this important detail in his comment below!

Being an oddball, the rather unstable perbromic acid ($\ce{HBrO4}$) was not in the list! 

It was synthesized by Evan Appelman (even on a larger scale) by bubbling fluorine gas through an alkaline solution of 1M $\ce{NaBrO3}$ and 5M $\ce{NaOH}$ until the solution becomes acid. 

Amazingly, the author further states in a footnote:


  The reaction is not smooth, and small explosions may take place in the vapor above the solution.