Application is not compatible with Galaxy Tab 3 (G

I uploaded an application to Play Store which I can't install on Samsung Galaxy Tab 3. It just tells me that device is uncompatible and no reason. I've checked in Developer's Console and it is also unsupported by Galaxy Tab 3 7.0, Galaxy Tab 4 and other tablets. Here's my manifest file:

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
    package="***"
    android:versionCode="2"
    android:versionName="1.0.1" >

    <uses-sdk
        android:minSdkVersion="14"
        android:targetSdkVersion="19" />

    <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />
    <uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE" />
    <uses-permission android:name="android.permission.ACCESS_NETWORK_STATE" />
    <uses-permission android:name="android.permission.ACCESS_WIFI_STATE" />
    <uses-permission android:name="android.permission.INTERNET" />
    <uses-permission android:name="android.permission.CAMERA" />
    <uses-permission android:name="android.permission.RECORD_AUDIO" />

    <application
        android:name="***.App"
        android:icon="@drawable/ic_launcher"
        android:label="@string/app_name"
        android:theme="@style/AppTheme" >
        <activity
            android:name="***.MainActivity"
            android:label="@string/app_name" >
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />

                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
        <activity android:name="***.DocumentInfoActivity" />
        <activity android:name="***.ReaderActivity" />
        <activity
            android:name="***.ImageOverviewActivity"
            android:theme="@style/Theme.Transparent" />
        <activity
            android:name="***.AccountsActivity"
            android:windowSoftInputMode="stateHidden" />
        <activity android:name="***.SearchHelpActivity" />
        <activity
            android:name="***.DeveloperSettingsActivity"
            android:label="@string/preferences_title" />
    </application>

</manifest>

As you can see there's nothing special which can influence on compatibility. Can there be some hidden reasons in code for example? How can I fix and test this?

I can install and run the app on SG Tab 3 avoiding Play Store.

I'm not 100% sure but it could be, that your front facing camera has no autofocus, thats why you'd have to add following in your AndroidManifest.xml:

<uses-feature android:name="android.hardware.camera.autofocus" android:required="false" />

please let me know, if this worked - cause, I'm pretty sure, that some persmissions are to restrictive

Edit:

you can test the modification, if you upload the new apk in alpha or beta mode. After some hours your test accounts will receve the update, but it's not published yet.