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Details on the Length/Coverage Optimal (LCO) confidence interval for the binomial proportion can be found in the following journal article:

Schilling, M., and Doi, J. (2014) 'A Coverage Probability Approach to Finding an Optimal
Binomial Confidence Procedure'
*The American Statistician*
, 68(3), 133--145
(Online access)

The
LCO website
contains the R code for the CI algorithm and a full listing of LCO CIs
(at 5 decimal places), for
*n*
= 1, 2, ..., 100 at the
90, 95, and 99% levels.