Generate a perfectly normally distributed sample of size n in R

Question

I would like to generate a sample of mean = 0, sd = 1 and size n = 100 which distribution is as normal as possible. Using rnorm alone returns a lot of variability.

The only way I found was to average multiple rnorms.

rowMeans(replicate(10000, sort(rnorm(100, 0, 1))))

This returns a rather satisfying result, but I'm not sure it's the most efficient way of doing it.

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EDIT:

I don't want the mean and sd to be strictly equal to 0 and 1, but rather, the distributin to "look" like a normal distribution (when plotting the density curve).

It seems that the qnorm method works worse than the "average" method:

# qnorm method
x <- qnorm(seq(.00001, .99999, length.out = 100), mean=0, sd=1)
plot(density(x))

# average method
x <- rowMeans(replicate(10000, sort(rnorm(100, mean=0, sd=1))))
plot(density(x))

I would be pleased with a deterministic solution returning results close to the average method in a more efficient way.

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EDIT 2 : Possible solution

Based on the answers, the following seems to work, adjusting the bounds relatively to n:

x <- qnorm(seq(1/n, 1-1/n, length.out = n), mean=0, sd=1)

Below a comparison of the qnorm and average methods for different values of n:

par(mfrow=c(6,2))
for(n in c(10, 20, 100, 500, 1000, 9876)){
  x <- qnorm(seq(1/n, 1-1/n, length.out = n), mean=0, sd=1)
  plot(density(x), col="blue", lwd=2)

  x <- rowMeans(replicate(10000, sort(rnorm(n, mean=0, sd=1))))
  plot(density(x), col="red", lwd=2)
}

Answer 1

You can use the bayestestR package:

library(bayestestR)
x <-  rnorm_perfect(n = 100, mean = 0, sd = 1)
plot(density(x))