(1) Var - closed form: 0 ;  E - closed form: 0
    d Var/E - H_d(p): 0
    H_d(1/d) = d*(d**3 + 8*d**2 - 12*d + 4)/((3*d - 2)*(5*d - 4)) ;  H_d(1/d) - d(d-1)/15 = d*(157*d**2 - 210*d + 68)/(15*(3*d - 2)*(5*d - 4))
(2) min over p-grid of tau_lumped(p)/H_d(p) (must be >= 1); tau_lumped(1/d) vs d(d-1)/15; min over {p: pd>=4} of tau_lumped(p)*3p/((1-p)d)
    d=   2: min tau_l/H = 1.0000 (at p=0.0001);  tau_l(1/d) =      1.681 >= d(d-1)/15 =     0.133;  min ratio (pd>=4) = nan
    d=   3: min tau_l/H = 1.0000 (at p=0.0001);  tau_l(1/d) =      2.675 >= d(d-1)/15 =     0.400;  min ratio (pd>=4) = nan
    d=   4: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =      3.874 >= d(d-1)/15 =     0.800;  min ratio (pd>=4) = nan
    d=   6: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =      6.963 >= d(d-1)/15 =     2.000;  min ratio (pd>=4) = 7.310
    d=   8: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =     11.108 >= d(d-1)/15 =     3.733;  min ratio (pd>=4) = 4.161
    d=  12: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =     22.951 >= d(d-1)/15 =     8.800;  min ratio (pd>=4) = 2.716
    d=  16: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =     39.765 >= d(d-1)/15 =    16.000;  min ratio (pd>=4) = 2.160
    d=  24: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =     88.563 >= d(d-1)/15 =    36.800;  min ratio (pd>=4) = 1.813
    d=  32: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =    157.663 >= d(d-1)/15 =    66.133;  min ratio (pd>=4) = 1.677
    d=  64: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =    637.530 >= d(d-1)/15 =   268.800;  min ratio (pd>=4) = 1.543
    d= 128: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =   2575.343 >= d(d-1)/15 =  1083.733;  min ratio (pd>=4) = 1.429
    d= 256: min tau_l/H = 1.0000 (at p=0.99);  tau_l(1/d) =  10366.839 >= d(d-1)/15 =  4352.000;  min ratio (pd>=4) = 1.373
all ok: True
