Spectrum of splitting 3-designs with block size 3×2

Abstract

Splitting t-designs were first formulated by Huber in recent investigation of optimal (t - l)-fold secure splitting authentication codes. In paper [M. Liang and B.Du, A new class of splitting 3-designs. Des. Codes Cryptogr., 60(2011), 283-290], it has been given that the necessary and sufficient condition for the existence of 3-(v, 3×2,1) splitting designs. In this paper, it will be completely determined that the spectrum problem of 3-(v, 3 × 2, λ) splitting designs, is that (1) λv(v - 1)(v - 2) = 0 (mod 48), (2) λ(v - 1)(v - 2) ∗ 0 (mod 8), (3) λ(v - 2) ∗ 0 (mod 2) and (4) v ≥ 6.