Optimal non-adaptive solutions for the counterfeit coin problem

We give optimal solutions to all versions of the popular counterfeit coin problem obtained by varying whether (i) we know if the counterfeit coin is heavier or lighter than the genuine ones, (ii) we know if the counterfeit coin exists, (iii) we have access to additional genuine coins, and (iv) we need to determine if the counterfeit coin is heavier or lighter than the genuine ones. Moreover, our solutions are non-adaptive.