Outward Remittance - (Indian Rupee to EUR) (Mumbai)

Just wanted to check if someone has done an Outward remittance from India (INR to EUR) without going to a private bank (like ICICI, HDFC). Their remittance rate for selling a Euro, compared to market rate is very poor.
Whether going to a Western Union, MoneyGram is more value. I checked Online sites (but seemingly there are restrictions of remittance from India subcontinent)
Any help/advice is appreciated

Thanks much
Sachin