Honestly, I never really paid much attention to Janet's panties other than that they were white, and low across the hips.
Jaimie F. has informed me that Janet wears
two different white undies (and I will absolutely take her word on that!) The ones in Touch-a are different than the dinner scene.
The Touch-a pair have some scalloped lace trim on them with white satin bows. There's also a small lacy trim around the leg holes. That side seam is probably no more than 3". They would most definitely have been Nylon.
I've never found any vintage panties just like them, but I've found similar styles from the 70s that have diagonal lace on the front. They seem to have the lace trim continuing from the side waist to the crotch seam or meeting in a "V" above the crotch seam.