I am making an URL shortener, and I am struggling with the optimal way of encoding a number (id) into a character string.

I am using the characters 0-9,A-Z,a-z so it will basically be a base-62 encoding. That is pretty basic, but it doesn't make use of all possible codes. The codes that it would produce would be:

0, 1, ... y, z, 10, 11, ... zy, zz, 100, 101, ...

Notice that the codes 00 to 0z is not used, the same for 000 to 0zz, and so on. I would like to use all the codes, like this:

0, 1, ... y, z, 00, 01, ... zy, zz, 000, 001, ...

It would be some combination of base-62 and base-63, with different bases depending on the position... Using base-62 is easy, for example:

create procedure tiny_GetCode
    @UrlId int
as
set nocount on

declare @Code varchar(10)
set @Code = ''

while (@UrlId > 0 or len(@Code) = 0) begin
    set @Code = substring('0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz', @UrlId % 62 + 1, 1) + @Code
    set @UrlId = @UrlId / 62
end

select @Code

But I haven't yet managed to make a multi-base conversion out of it, to make use of all the codes.