boms.py

# Based on: https://github.com/Bekbolatov/SortingNetworks/blob/master/src/main/js/gr.js
def boms_get_partner(n, l, p):
    if p == 1:
        return n ^ (1 << (l - 1))
    scale = 1 << (l - p)
    box = 1 << p
    sn = n//scale - n//scale//box*box;
    if sn == 0 or sn == (box - 1):
        return n
    if (sn % 2) == 0:
        return n - scale
    return n + scale

def boms_pairs(d):
    A = []
    for l in range(1, d+1):
        for p in range(1, l+1):
            Y = set()
            for n in range(2**d):
                partner = boms_get_partner(n, l, p)
                if partner != n:
                    if partner > n:
                        partner1 = n
                        partner2 = partner
                    else:
                        partner1 = partner
                        partner2 = n
                    Y.add((partner1, partner2))
            A.append(Y)
    return A

print(boms_pairs(3))