Monte Carlo Sizing & BIBD Randomization

I need a reproducible Monte Carlo simulation in R that pins down the required sample size for an object-case Best–Worst Scaling study analysed with a conditional logit model. The design has 12 outcomes, shown 4 at a time across 12 choice tasks per participant.

Both clinical feasibility and scientific defensibility carry equal weight, so the simulation must iterate half-width targets of 0.5, 0.4 and 0.3 for the 95 % confidence interval around the difference between the highest and second-highest preference weights. Please report the smallest sample that satisfies each target along with power curves and the logic behind the stopping rules.

The 12 outcomes will be shown in a pre-determined sequence. To support that, I also need a Balanced Incomplete Block Design that allocates the 12 outcomes into the 12 tasks (4 per task) and a randomisation list that can be fed straight into fielding software.

Deliverables
• Annotated R script(s) that run the simulation and export summary tables/plots
• Brief technical memo explaining assumptions, convergence checks and final recommendations
• CSV/Excel file containing the BIBD task × outcome matrix plus participant-level randomisation sequence
• Short README so the research team can reproduce everything with a single command