Very white in my garden is a small diploid - 'Silver Run' (Lee, 1989). It is a prolific bloomer and very fertile.
A tet that is a great pod setter with hot pollen is 'Spacecoast White Chocolate' (Kinnebrew-J., 2007)
'White Mountain' (Stamile, 2006) is a heavy blooming tet that easily sets both ways.