What is an alternate of ionic zip in C#?

If you can use .NET Framework 4.5+, ZipArchive is now part of the BCL, as described by the "What's New in the .NET 4.5 Base Class Library" article.

Also, IMHO the 'de facto' third-party library for this is SharpZipLib from the SharpDevelop team.

It can actually handle larger files.

For that you need to use property:

UseZip64WhenSaving = Zip64Option.Always