NEWS.md

In PGM2: Recursive Construction of Nested Resolvable Designs and Associated Uniform Designs over GF(p)

PGM2 2.0.1

Bug fixes

• Uniform() no longer depends on the order of the blocks. The previous first-fit greedy extraction of parallel classes could fail on a valid resolvable design presented in an unfavourable row order: of 200 random row permutations of the 28-block design of Example 3 of Boudraa et al. (2013), 178 raised an error. The resolution is now found by exact-cover search with backtracking over the whole partition, so any row permutation yields the same design up to a permutation of the factors and a relabelling of levels. Designs produced by the package's own constructors are unchanged.
• Uniform() validates its input and reports clearly when a matrix cannot be resolvable (block size not dividing the number of treatments, a repeated treatment within a block, or no resolution), instead of returning a partial design or failing with an internal subscript error. It also gains a classes component listing the row indices forming each parallel class.
• Steps() rejects unknown or empty stage values instead of silently returning an empty list.

Documentation

• The complexity note for Qn() now reflects the labelling step as well as the subspace enumeration, and states that timings are hardware dependent.
• The Qn() help page states the Plackett-Burman identification precisely, up to row, column and level equivalence.

PGM2 2.0.0

Major generalisation: the whole construction now works over GF(p) for any prime p, as in the theory of Boudraa, Gheribi-Aoulmi & Laib (2013). Versions <= 1.2 implemented only p = 2.

New features

• New function Qn(m, n, p = 2): builds the reduced resolvable design Q*_n of stage n directly, with its associated uniform design U(p^m, (p^n)^r) — the design of the 2013 paper's Example 3, previously constructible only by hand. Any two runs coincide in a constant number of factors (equidistance), so every stage attains the discrete-discrepancy lower bound of Fang et al. (2004), and levels refine across stages.
• BIB(m, p = 2) and Steps(m, n, stage, p = 2) gain a p argument (prime; checked). Gen() and Resolvable() are now order-agnostic: block sizes are derived from the data instead of binary-only formulas.
• BIB() additionally returns Lambda, the concurrence parameter.
• A test suite validates every construction against the parameters published in Tables 1 (p = 2) and 2 (p = 3) of the 2013 paper, checks balance (constant r and lambda over all pairs), actual resolvability (partition into parallel classes) and level balance of the uniform designs.
• A vignette reproduces all worked examples and both tables of the paper.

Backward compatibility

• For p = 2 (the default), BIB(), Gen(), Resolvable() and Uniform() return exactly the same designs as version 1.2 (this is enforced by a regression test against the 1.2 algorithm).
• Steps() now returns a tidy named list (BIB1, BIBg, Resolvables, UDs, each stage a proper sub-list) instead of the flat, partially unnamed splice of previous versions.
• Uniform() no longer emits recycling warnings (an internal placeholder row was removed); results are unchanged.
• Input validation: BIB() rejects non-prime p and m < 2 with clear error messages.

PGM2 1.2

• Last GF(2)-only release (CRAN, 2025-05-27).

PGM2 documentation built on Aug. 27, 2026, 9:07 a.m.