squarelattice

is the required block size and is the integer square root of the required number of treatments

is is the required number of replicates

Internal function constructs square lattice designs for resolvable nested block designs with 
v*v treatments, r complete replicate blocks and nested blocks of size v.
Returns a simple lattice with r = 2 or a triple lattice with
r = 3 for any size of v.
Returns a quadruple lattice with r = 4 for any v &lt;= 30.
Returns a lattice for any r &lt; v + 2 if v is a prime or prime power with p^q less than or equal to:<ul>
<li>2**12</li>
<li>3**7</li>
<li>5**5</li>
<li>7**4</li>
<li>(11,13,17,19)**3</li>
<li>(23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97)**2</li>
</ul>

internal

Constructs treatment and block designs for linear treatment models
with crossed or nested block factors. The treatment design can be any feasible
linear model and the block design can be any feasible combination of crossed or
nested block factors. The block design is a sum of one or more block factors
and the block design is optimized sequentially with the levels of each successive
block factor optimized conditional on all previously optimized block factors.
D-optimality is used throughout except for square or rectangular lattice block designs
which are constructed algebraically using mutually orthogonal Latin squares.
Crossed block designs with interaction effects are optimized using a weighting scheme
which allows for differential weighting of first and second-order block effects.
Outputs include a table showing the allocation of treatments to blocks and tables showing
the achieved D-efficiency factors for each block and treatment design.
Edmondson, R.N. Multi-level Block Designs for Comparative Experiments.
JABES 25, 500<e2><80><93>522 (2020) <doi:10.1007/s13253-020-00416-0>.

squarelattice: Square lattice designs

Description

Usage

Arguments