How can I achieve higher quality results from my bargain based 4K monitor?
Here is some information:

Apple lists the 2013 MacBook Pro with Intel Iris Technology as being able to run a 4K display at 4096-by-2160 resolution and 24 Hz as well as 3840-by-2160 displays at 30 Hz over its HDMI port. 

The latter is the resolution of the Seiki and conveniently as high as it goes at 4K – HDMI 1.4 is limited at these rates. 

Some manufacturers say that they will update their HDMI 1.4 to 2.0 which can do higher frame rates, but Seiki has made no such promise.