molecular biology - What is the highest competency possible for E coli?

This is a great question as I just made my own "homebrew" chemically competent cells.

There are a vast variety of E. coli strains that are commonly used for cloning. They may be transformed chemically by heat shock method, or electrically by electroporation (a brief summary may be found here). These can be made in the lab manually, or purchased commercially from reputable vendors (I recommend Invitrogen/Life Tech, NEB, Promega).

Chemically competency is achieved using Hanahan's method or some a variation thereof. The method involves washing the bacteria in a series of buffers containing various di-valent cation chloride salts (CaCl₂, RbCl₂, etc). Commercially available E. coli are sold as "regular" and "ultra" competent, ranging from 10⁶ to 10⁶ for regular, and the highest I've seen is 10¹⁰ cfu/µg DNA. For maximum efficiency, especially since a small plasmid such as yours will be easy to transform, electroporation is a more efficient technique, but requires specialized equpment. Electroporation can yield >10¹⁰ cfu/µg. For standard cloning practices, regular or high efficiency chemically competent E. coli are perfectly adequate. Since you mentioned you are creating a library, you certainly want to go with ultra high efficiency chemical transformation or, if you have the necessary equipment, electroporation. I have not seen electroporation efficiencies reported > 5x10¹⁰.

Transformation efficiencies are standardized by reporting a rate as the number of colony forming units (cfu) per µg of some control plasmid, typically pUC19. Transformation efficiency is very sensitive to many factors, including heat shock time, cooling times, thawing time, amount and size of plasmid DNA. All things being equal, the size and quantity of DNA are important for your purposes. Transformation efficiency generally increases with quantity of DNA, but there is a saturation point, and evenetually having too much DNA decreases the yield. Also, efficiency decreases linearly with plasmid size. For example, pUC19, the control vector, is ~2.7 kbp, and your library plasmid is ~6.6 kbp, so you should expect for the same mass of DNA you will have lost 60% transformation due to plasmid size. This loss is due to the physically larger size of DNA being more difficult to move into the bacteria.