Lotto design tables

An LD(n,k,p,t;b) lotto design is a set of b k ‐sets (blocks) of an n ‐set such that any p ‐set intersects at least one k ‐set in t or more elements. Let L(n,k,p,t) denote the minimum number of blocks in any LD(n,k,p,t;b) lotto design. We will list the known lower and upper bound theorems for lotto designs. Since many of these bounds are recursive, we will incorporate this information in a set of tables for lower and upper bounds for lotto designs with small parameters. We will also use back‐track algorithms, greedy algorithms, and simulated annealing to improve the tables. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 335–359, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10020