% 
M = 200;
N = 1e12;
P = N / M;
s = 10;
epsilon = 1e-5;

x = 22:0.2:30;
N = zeros(size(x));
P = zeros(size(x));
sigma = zeros(size(x));

for i = 1: length(x)
    N(i) = 10^x(i);
    P(i) = N(i) / M;
    ita_1_lb = sqrt(172.24 * 32.0 * s * (log(4 * s) ^ 2) * log(8 * N(i)) * log(9 * P(i)) / P(i));
    ita_2_lb = sqrt(32.0 / 3.0 * s * (-log(epsilon)) / P(i));
    sigma(i) = ita_1_lb * (1 + ita_1_lb) + ita_2_lb;
end

semilogx(P, sigma);