A family of symmetric designs

Abstract An embedding theorem for certain quasi-residual designs is proved and is used to construct a series of symmetric designs with υ = (1 + 16 + ⋯ + 16 m )9 + 16 m +1 , k = (1 + 16 + ⋯ + 16 m )9, and λ = (1 + 16 + ⋯ + 16 m -1 )9 + 16 m ·3, for a non-negative integer m .