Remember this rule: c1v1=c2v2
c is concentration and v is volume. In this case you know c1 (100 mg/mL), c2 (3, 6, 12, 18 mg/mL), and v2 (15mL). You want to solve for v1 therefore the equation would be v1=(c2v2)/c1
Starting with the 18 mg you would have v1=(18mg/mL*15mL)/100 mg/mL. Solving, you would need 2.7 mL of 100mg/mL nicotine base diluted to 15 mL in "everything else". For 12 mg/mL you would need 1.8 mL, 6 mg/mL you need 0.9 mL, and 3 mg/mL you need 0.45 mL.
Water is approximately 20 drops/mL but that is a really inaccurate measurement. I would suggest running by the pharmacy and get some syringes in varying volumes. Be honest and tell the pharmacist what you're doing and they will be more than happy to help you.