I am planning to construct a new bicycle. But i have a very low budget. Its more like a challenge for me. Please help
Depends on what you mean by "construct". Do you want to purchase all the various parts and assemble it, find an existing bike and change it around to suit what you want to have, manufacture actual parts?
You will never be able to put together a complete bike cheaper than what a large company can do (unless you want to build something radically different than what is commonly available.) Building something of quality at low cost, it is very hard to beat buying a used bike and making whatever changes are desired.
But if you have a specific goal in mind (cheap transport, a specific look/style, the experience of assembling a bike from scratch, etc.) let us know and maybe we can give you some ideas.