How to define an efficient lookup table?

Question

I want to create a table that will act as a lookup table for an application.
The format I have in mind is something like:

CREATE TABLE Associations (
  obj_id int unsigned NOT NULL,
  attr_id int unsigned NOT NULL,
  assignment Double NOT NULL
   PRIMARY KEY (`obj_id`, `attr_id`),
);  

Anyway I have the following question:
The idea is that this table will be loaded/used in the application level as a map:
obj_id -> listof(<attr_id, assignment>)

The obj_id refers to another table which is huge. Now this means that Associations will be x times the original table since we'll have multiple rows for each obj_id.
Taking into account that I don't really need to SELECT in the table by assignment and at this point I also don't need to SELECT by attr_id is there another design approach for the table that could be more efficient?