My two best rounds ever have one thing in common...very little sleep the night before. Mind you, this is loose correlation and not causation.
The last round was recently and it was on a weekday afternoon/evening round and I was pretty close to bowing out because I was so tired.
The lowest round I've ever shot was 63 on a par 70. But the round that felt even better was shooting 64 on a par 72 course with a rating of 73.1. A few things stick out from that round in particular:
1. First of all it was a very clean straightforward card. 8 birdies and 10 pars... no bogeys, no doubles, no eagles.
2. I hit one God awful tee shot that day that should have been OB, but instead hit the roof of a house and bounced all the way back into the fairway. I got up and down for a birdie so that was a minimum 3-shot swing right there.
3. I'm sure I made almost 200 feet of putts that day. My iron game wasn't particularly sharp, but I was rolling it like the best.
4. On 18 (par 5) I hit my 2nd shot off a greenside sprinkler head and it careened into the water hazard. After my drop I ended up holing the next shot for birdie. So an unlucky bounce was immediately repaid... which never happens for me
5. I was 3 under at the turn and almost made a hole in one on 10. That's when I knew it would be a special day. At the next hole (tight fairway with hazard on both sides) where I normally hit a low iron off the tee, I pulled driver and smoked it down the middle
Since then I haven't shot 64 again or even 65. The best I've done is 66 (-6) with a few 67s and a number of 68/69 (along with plenty of 72-76).