Resolvable BIBDs with block size 7 and index 6

Abstract

A necessary condition for the existence of a resolvable balanced incomplete block design on v points with k=7 and λ=6 is that v≡0 mod 7 . This condition is shown to be sufficient for v>462, with 18 possible exceptions plus one known exception (v=14) below this value. Also considered are the existence of (v,7,6)-NRDs, (7,6)-frames of type 7 t and (7,6)-resolvable GDDs of type 7 t .