Some good but not optimum sets
Karnac
You may want to consider the following 15-number sets (always based on 2186 drawings):
1-2-3-4-5-6-7-8-10-11-14-18-27-30-35 which gives 42x5-winning numbers, 19x6-winning numbers and 0x7-winning numbers
or
1-2-3-4-5-6-7-8-9-18-22-27-40-43-47 which gives 80x5-winning numbers but only 3x6-winning numbers and 0x7-winning numbers.
I also remember seeing one set that gave 6x7-winning numbers but I have lost that information.
These compare favorably with Nick's set (1-7-13-15-19-27-29-30-31-34-40-43-45-46-49) resulting in 40x5-winning numbers, 19x6-winning numbers and 0x7-winning numbers. But Nick has a definite advatage in the time required to obtain a good set.
I do not think all combinations can be verified unless you own a super computer. The possibilities are so huge, COMBIN(49,15), that it is nearly impossible to go through all combinations but Nick's approach is certainly a step in the right direction. Most likely the optimum set (however it is defined) may never be determined with 100% certitude but some excelent sets could be identified.