Nothing
runif.faure <- function(n,dimension){
pr <- c(2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,
61,67,71,73,79,83,89,97,101, 103,107,109,
113,127,131,137,139,149,151,157,163,167,173,
179,181,191,193,197,199,211,223,227,229,233,
239,241,251,257,263,269,271,277,281,283,293,
307,311,313,317,331,337,347,349,353,359,367,
373,379,383,389,397,401,409,419,421,431,433,
439,443,449,457,461,463,467,479,487,491,499,
503,509,521,523,541,547,557,563,569,571,577,
587,593,599,601,607,613,617,619,631,641,643,
647,653,659,661,673,677,683,691,701,709,719,
727,733,739,743,751,757,761,769,773,787,797,
809,811,821,823,827,829,839,853,857,859,863,
877,881,883,887,907,911,919,929,937,941,947,
953,967,971,977,983,991,997)
# base of number system
r <- pr[pr>=dimension][1]
# compute coefficients
# a priori upper bound for the length of the sequence
m <- ceiling(log(n)/log(r))
C <- matrix(0,m,m)
C[1,] <- 1
for (j in 2:m){
C[j,j] <- 1
if ((j-1)>=2){
for (i in 2:(j-1)){
C[i,j] <- C[i,(j-1)] + C[(i-1),(j-1)]
}
}
}
C <- C%%r
# to do the radical inverse
dg <- r^(-(seq(1,m,1)))
F <- matrix(0,n,dimension)
for (i in 1:n){
# base r decomposition
nr <- matrix(0,m,1)
number <- i
for (k in 1:m){
quo <- floor(number/r)
res <- number - quo*r
number <- quo
# i = nr(m)*r^(m-1) + ... + nr(2)*r + nr(1)
nr[k] <- res
}
F[i,1] <- sum(dg*nr)
for (j in 2:dimension){
nr <- (C%*%nr)%% r
F[i,j] <- sum(dg*nr)
}
}
# outputs
return(out=list(design=F,n=n,dimension=dimension))
}
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