filling seeds in latin hypercube - lhs for r

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having an simple latin hypercube

mylhs<-randomLHS(3, k=2)
plot(mylhs,ylim=c(0:1),xlim=c(0:1),pch="+")
abline(v=1/3)
abline(v=2/3)
abline(h=1/3)
abline(h=2/3)

I want to augment it by 6 more seeds so that in every cell is at least one. The next step would be to add 9 seeds more, so that in every cell are exactly 2. For knowing what I mean by cell, it might help to draw the plot and lines

that's probably not the original idea of lhs, but is it possible?

the augmentLHS doesn't full fill the task (only by accident)

mylhs2<-optAugmentLHS(mylhs, m=6)
points(mylhs2,col="red")
abline(v=1/3)
abline(v=2/3)
abline(h=1/3)
abline(h=2/3)
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