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#' @name blocksdesign-package
#' @title Blocks design package
#' @aliases blocksdesign
#' @docType package
#'
#' @description The \code{blocksdesign} package provides functionality for the construction
#' of block and treatment designs for general linear models.
#'
#' @details
#'
#' Randomized complete blocks are the designs of choice for small experiments with few treatments.
#' For large experiments with many treatments, however, a single set of complete blocks may not be adequate
#' and then sub-division into smaller nested blocks may be required. Block designs with a single level of nesting are
#' widely used but a single level of nesting may be inadequate for very large experiments with many treatments.
#' \code{blocksdesign} provides for the construction of designs with multiple levels of nesting down to any
#' feasible depth of nesting.
#'
#' Sometimes block designs for the control of variability in two or more dimensions are required and
#' \code{blocksdesign} can also build crossed block designs allowing for both additive and interactive crossed
#' block effects simultaneously.
#'
#' The \code{blocksdesign} package has two main functions:
#'
#' i) \code{\link[blocksdesign]{blocks}}: This is a simple recursive function for nested blocks for
#' unstructured treatments. The function generates designs for treatments with arbitrary levels of replication
#' and with arbitrary depth of nesting where blocks sizes are assumed to be as equal as possible for each level of nesting.
#' Special square and rectangular lattice designs (see Cochran and Cox 1957) are constructed
#' algebraically from mutually orthogonal Latin squares (MOLS). The outputs from the \code{blocks} function include a data
#' frame showing the allocation of treatments to blocks and a table showing the achieved D- and A-efficiency factors for each
#' set of nested blocks together with A-efficiency upper bounds, where available. A plan showing the allocation of treatments
#' to blocks for the bottom level of the design is also included in the output.
#'
#' ii) \code{\link[blocksdesign]{design}}: This is a general purpose function for linear models with qualitative
#' or quantitative level treatment factors and qualitative level block factors. The function finds a D-optimal
#' or near D-optimal design for a specified treatment model and then finds a conditional D-optimal or
#' near D-optimal block design for that choice of treatment design. The \code{design} algorithm builds the blocks design
#' by sequentially adding \code{blocks} factors where each blocks factor is optimized conditional on all previously
#' added \code{blocks} factors. The outputs include a data frame of the block and treatment factors for each plot and a table
#' showing the achieved D-efficiency factors for each set of nested or crossed blocks.
#' Fractional factorial efficiency factors based on the generalized variance of the complete factorial design are also shown.
#'
#' Other available functions are \code{\link[blocksdesign]{A_bound}}, which finds upper A-efficiency bounds for regular
#' block designs, \code{\link[blocksdesign]{MOLS}}, which constructs sets of mutually orthogonal prime-power
#' Latin squares (MOLS), \code{\link[blocksdesign]{GraecoLatin}}, which constructs mutually orthogonal Graeco-Latin
#' squares not necessarily prime-power, \code{\link[blocksdesign]{isPrime}}, which tests an integer for primality,
#' \code{\link[blocksdesign]{isPrimePower}}, which factorizes prime powers and \code{\link[blocksdesign]{HCF}},
#' which finds the highest common factor (hcf) for a set of positive integer numbers.
#'
#' For further explanation see Edmondson (2020) and \code{vignette(package = "blocksdesign")}.
#'
#' @references
#'
#' Cochran W. G. & Cox G. M. (1957) Experimental Designs 2nd Edition John Wiley & Sons.
#'
#' Edmondson, R.N. Multi-level Block Designs for Comparative Experiments. JABES 25, 500–522 (2020).
#'
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