Add sliced and nested Latin hypercube designs

[bertcarnell]

Summary

Adds two new design-generation methods to the package, filling a gap in supported design types (previously there was no way to create designs with a slice/subset structure):

• slicedLHS(m, t, k) — a sliced Latin hypercube design (Qian, 2012) made up of t slices of m points each. Every slice is itself a Latin hypercube design, and the union of all slices is a Latin hypercube design of n = m*t points. Useful for computer experiments mixing quantitative and qualitative factors (one slice per level combination) and for collecting data in batches. Slice membership is returned in the "slices" attribute of the result.
• nestedLHS(small, large, k) — a nested Latin hypercube design (Qian, 2009) in which the small-point design is a subset of the large-point design and both are valid Latin hypercube designs. Useful for two-level / multi-fidelity computer experiments. Returns a list with $small and $large, where $small is the first small rows of $large.

Both are implemented in pure R (the constructions are simple combinatorial assignments), matching the style of the existing augmentLHS.

What's included

• R/slicedLHS.R, R/nestedLHS.R with roxygen documentation
• Generated man pages man/slicedLHS.Rd, man/nestedLHS.Rd
• NAMESPACE exports
• testthat tests (tests/testthat/test-slicedlhs.R, test-nestedlhs.R) covering the Latin properties of the union/slices/subsets and input validation, using the existing checkLatinHypercube helper
• NEWS, README (.Rmd + .md) entries, updated package Description, and a version bump to 1.4.0

Verification

R is not available in the build environment used to prepare this branch, so the testthat suite was not executed here — please run R CMD check / devtools::test() before merging. The construction algorithms were validated by porting them to an independent script and confirming, over 2000 randomized trials each, that:

• sliced: the union and every individual slice are valid Latin hypercube designs
• nested: both the large and small designs are valid Latin hypercube designs and the small design is exactly the first small rows of the large design

References

• Qian, P. Z. G. (2012) Sliced Latin Hypercube Designs. JASA 107, 393–399.
• Qian, P. Z. G. (2009) Nested Latin hypercube designs. Biometrika 96, 957–970.

Notes / possible follow-ups

• nestedLHS implements the canonical two-layer case (large must be an integer multiple of small). A multi-layer chain (n_1 | n_2 | ... | n_L) could be a future extension.
• The man pages were hand-written to match roxygen2 output since R wasn't available to regenerate them; re-running roxygen2::roxygenise() should produce an identical result.

https://claude.ai/code/session_01JNVgdYk9zNB8B4hLSn8rzj

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