@techreport{d3e5ff9305d340178c59f508fd7d6cdb,

title = "Two-Dimensional Minimax Latin Hypercube Designs",

abstract = "We investigate minimax Latin hypercube designs in two dimensions for several distance measures.For the l-distance we are able to construct minimax Latin hypercube designs of n points, and to determine the minimal covering radius, for all n.For the l1-distance we have a lower bound for the covering radius, and a construction of minimax Latin hypercube designs for (infinitely) many values of n.We conjecture that the obtained lower bound is attained, except for a few small (known) values of n.For the l2-distance we have generated minimax solutions up to n = 27 by an exhaustive search method.The latter Latin hypercube designs will be included in the website www.spacefillingdesigns.nl.",

keywords = "minimax, Latin hypercube designs, circle coverings",

author = "{van Dam}, E.R.",

note = "Subsequently published in Discrete Applied Mathematics, 2008 Pagination: 13",

year = "2005",

language = "English",

volume = "2005-105",

series = "CentER Discussion Paper",

publisher = "Operations research",

type = "WorkingPaper",

institution = "Operations research",

}