I felt so stupid! I convert the 160cm into inches and realize my luggage are not oversized.

That said. Should I purchase assigned seat on Shinkansen? They cost a little more. Does non-reserved ticket still mean I can get on the train and I will have a seat somewhere?

(However, I have another 28" luggage that is actually close to 65" combined, so it is going to be over 160cm. I am not sure how strict Shinkansenis. I don't want to find out. I will stick to my smaller 28")