I think the Base iOS 9 SDK is requied for Xcode 8.
Please try following steps to install iOS 9.3 Base SDK:
1) Download Xcode_7.3.1.dmg from
https://developer.apple.com/downloads/
2) Mount it
3) Copy SDK from
/Volumes/Xcode/Xcode.app/Contents/Developer/Platforms/iPhoneOS.platform/Developer/SDKs/iPhoneOS.sdk
to
/Applications/Xcode.app/Contents/Developer/Platforms/iPhoneOS.platform/Developer/SDKs/iPhoneOS9.3.sdk
4) Copy Simulator from
/Volumes/Xcode/Xcode.app/Contents/Developer/Platforms/iPhoneSimulator.platform/Developer/SDKs/iPhoneSimulator.sdk
to
/Applications/Xcode.app/Contents/Developer/Platforms/iPhoneSimulator.platform/Developer/SDKs/iPhoneSimulator9.3.sdk
5) Run command in shell
sudo /usr/libexec/PlistBuddy -c "Set :MinimumSDKVersion 9.3" /Applications/Xcode.app/Contents/Developer/Platforms/iPhoneOS.platform/Info.plist
6) Run command in shell
sudo /usr/libexec/PlistBuddy -c "Set :MinimumSDKVersion 9.3" /Applications/Xcode.app/Contents/Developer/Platforms/iPhoneSimulator.platform/Info.plist
7) Restart Xcode
8) Open Xcode project setting->Build Settings->Base SDK, then Select iOS 9.3 option.
9) Rebuild application