The lines on the square military chutes for HALO or miitary freefall are a newer material like Dyneema or similar material. Not too familiar with them as they are after my time in service.

You have to remember, nylon was the wonder fabric several decades ago. It is still strong for it's weight and a good material for parachute lines on standard round parachutes. The reason square chutes have evolved to newer, lighter materials is to cut down on bulk and weight. Most squares are packed with the reserve in the same backpack container and it is still very light and compact compared to a military, round paratrooper parachute such as the T-10.