Orthogonal quadruple systems and 3-frames

Orthogonal quadruple systems are defined and investigated. Orthogonal quadruple systems with an additional nesting property are shown to provide a new construction of 3-frames F(3,4,n{2}) (Design Codes Cryptogr. 4 (1994) 5). Constructions for pairs of nested orthogonal quadruple systems are provided. Applications to 2-resolvable Steiner quadruple systems and highly nonlinear functions are discussed.