Compress transaction hex string I realized transaction hex can be very long and you need it for broadcasting a tx using blockstream.info API:
https://blockstream.info/testnet/api/tx

https://github.com/Blockstream/esplora/blob/master/API.md
If the user wants to send this hex using text message which allows 160 characters in one message, what should be the best way to solve this problem? I tried researching about way to compress it, send to a number which forwards to the web server running a PHP code, the hex string is decompressed and sent to blockstream.info for broadcasting tx. Base64 encoding after gzcompress() couldn't reduce the number of characters to less than 160.
Example:
Hex:02000000000101e939fb23e9991ebbc75fd08c736da32ca12d98a4ff1b8e970e97f5661927ee410100000000fdffffff02b0a90a000000000016001421e2f997b3bd36e273eaca365da8515a389444ae40420f0000000000160014829e2dbcf6b7f31bc93633971f71f6f6b9b5f89e0247304402200f8e3e573be749caf1964a85707bf540de2e7b367ae46c23bd4f21932ff82346022062dc3007072cd5a19b45e479525f4829bc48be4fd3c21b5a9ae34bcf9a3a3ccf0121020f88c7db36cbb492e80d3062fc19db55bed82687498f8cfe6d0cf47adf6687aa49f31b00
Compressed and Base64 encoded:
eNpdkNmJBEAIRFPyarsNxzP/ENZZGBZW9Eew6pVA8C0EbGObIG4zw47Ie6bg5WUtZ0pHKnsuMxiv7cLOHFU0ut2yCl+xqfktoAA3cPiz0R0hbBqzGxzF2nS5PZ31lL+Dx/mZiHgLCMH8v35kTRU5GncYI42V2S7Otu7W4syzBpLLIAK0Mec197kcfcXSB01lzS7cmCNQTb04etdUk5ZLhtCYZh6x6EdDqZIB9oSyjqOFnJZrh858oCLlRcsUJ2EcN2+WxTRn58wBJITN8/altV4ZIUb9oHi1J9EqzomuR/qW8s3LaS3Ikes1ult3sU9mgB8sW3Vy
Compressing a more-or-less random number is futile. Your best option is simply to use a more compact encoding. Base64 is better than Hex but there exists may other encodings that prform better
Wikipedia lists many and ranks them in order of efficiency
Encoding            Data type                    Efficiency
yEnc                Arbitrary, mostly non-text   ~98%
Ascii85             Arbitrary                     80%
Base85 (RFC 1924)   Arbitrary                     80%
Base64              Arbitrary                     75%
...

You can obviously do better if you use 8-bits (e.g. Unicode printable code points that have single byte encodings in UTF-8) but since SMS uses a 7-bit character set (so far as I know) you won't do much better