check: a = (1,1)/sqrt2 gives E|L| = sqrt2 (1-q) 2 tau  (q = 0.25, 0.29, 0.3, 1/3, 0.36)
max over unit a in R^n, n <= 7, of E|L| / (2 tau)  (1 = Theorem K tight at dictators)
q = 0.2800: max ratio 1.0182338   (per n: 1.01823, 1.01823, 1.01823, 1.01823, 1.01823, 1.01823)   maximiser |a| = [0.7071 0.7071]
q = 0.2900: max ratio 1.0040916   (per n: 1.00409, 1.00409, 1.00409, 1.00409, 1.00409, 1.00409)   maximiser |a| = [0.7071 0.7071]
q = 0.2929: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.2950: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.3000: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.3100: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.3200: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.3300: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.3400: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.3500: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.3600: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.3700: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
q = 0.3750: max ratio 1.0000000   (per n: 1.00000, 1.00000, 1.00000, 1.00000, 1.00000, 1.00000)   maximiser |a| = [1.]
