I know this is a late answer, but it can help others who are facing a similar problem:
Since recently (September 2015), you can download APKs up to 100 MB , if you are targeting Android 2.3 and higher, you can learn more about this help page . This limit was 50 MB. There is also an Android blogspot developer article explaining the changes here .
Alternatively, or if your application exceeds the APK limit of 100 MB, you can use extension files . These are additional files that are downloaded after installing your application and can be up to 4 GB (in particular, you can have two extension files up to 2 GB each). You can learn more about extension files on this page on the Android developers website .
However, note that there are some restrictions on the use of extension files, in addition to the limit of 2 GB per file, for example, the fact that the user must download your application via Google Play. More information on this can also be found on the Android Developers page above.
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