As far as I remember 5/16 also, but I would make some with 3/8,..just to see what they prefer,.. have seen natural holes in old trees, ...I don't think size is too critical.

This one is doing spring cleaning, looks like about 3/8" hole or larger.
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Leafcutter bees, also called alfalfa bees, nest in 1/4-inch diameter tubes but will use the same size holes as will masons.

see this
http://snohomish.wsu.edu/garden/masonbees/inse006.htm

Here is a link that might be useful: masons & alfalfa bees

They seem to prefer a 1/4 inch hole, that is the approximate size of commercial nesting boards used in alfalfa seed production. Leafcutters require approximately 21 days of 80 degrees or better to hatch in the spring, which brings them out in mid to late June after fruit trees have bloomed and they really aren't active until the air temperature gets above 70 degrees--making them a summer bee.

great info! 1/4" - 5/16" holes should keep them happy.
is there a rule of thumb as to how far apart these holes should be? with the straws they are no further than an 1/8" apart and with the blocks of wood they appear to be 3/4"-1" apart. does it really matter?