The "Trilene" knot pretty much the connection that all the Socal long range guys tie.
Uses: The Trilene Knot is a strong and reliable knot to join monofilament line to hooks, swivels and lures. It resists slippage and failures.
Tying it: When trimming the tag end, leave about an eighth of an inch for security.
Advantages: The double wrap of line through the eye takes some of the strain and may be responsible for claims that this knot retains a high proprtion of ideal line strength. This is more likely when the thickness of the eye is greater than the line diameter.
For big fish I have come to trust no knot other than the bimini twist (100% of line strength). The double line thus formed can be joined to your swivel with an offshore swivel knot which guarantees that if either leg of the double line breaks, you are still attached. Many people shy away from the bimini because it looks difficult, but it is one of the easiest knots I know. The Trilene and uni knots are harder to tie and more likely to fail unless tied perfectly.
The knot I have been using for years is now known as the Berkley Braid knot. It's not that they invented it, it has been around for many, many years but I guess they like it for braid lines so they "stole" the name. Tied correctly, I have not seen it fail.