function [v,sd] = ball(n,N)

M=20;  
a=[]; 

for k=1:M               % M independent runs
    x=2*rand(n,N)-1;    % random vectors in W_n
    nq = sum(x.^2 , 1); % list of the 2-norms (squared) of the vectors
    K = sum(nq<1);      % number of vectors with norm <=1    
    a = [a,K/N];        % percentage of points in B_n
end

a_m = mean(a);          % mean value of a
a_sd = std(a);          % standard deviation of a

v = a_m * 2^n;          % mean value of v
sd = a_sd * 2^n;        % standard deviation of a