Huge List<double> save in small file

I am trying to save a huge list of doubles in a file. For now it looks like this:

try{
       FileStream fs = new FileStream(saveFileDialog.FileName, FileMode.OpenOrCreate);                   
       using(BinaryWriter binaryWriter = new BinaryWriter(fs))
       {
             foreach (double value in bigData)
             {
                  binaryWriter.Write(value);
             }
             binaryWriter.Close();
        }
        fs.Close();
} catch(System.IO.FileNotFoundException)
{
    MessageBox.Show("Unexpected save error\n", "Save error!", MessageBoxButtons.OK);
}

bigData is a List<double> and in test case it contains 2 millions objects.

The saved file has around 15MB, which I think is quite a lot for only binary data. Has anyone got any idea, how I can make it much smaller?

Also, remember, that I need to open this file after saving - but this is done in another method.