Some results on lotto designs
Li, Ben Pak Ching
Given parameters 'n, k, p, t', an ('n, k, p, t ') Lotto design is a collection of 'k'-sets, such that any arbitrary 'p'-set, which are chosen from an 'n'-set, intersects at least one 'k'-set in the collection in at least ' t' elements. The number 'L'('n, k, p, t') is size of the minimal ('n, k, p, t') Lotto design. We prov de constructions and techniques for determining upper and lower bounds for ' L'('n, k, p, t'). We also provide computer programs that generate upper bounds for 'L' ('n, k, p, t').