On the non-existence of some Steiner t-(υ, k) trades of certain volumes

Abstract

Mahmoodian and Soltankhah [6] conjectured that there does not exist any t-(v,k) trade of volume s_i < s < S_i+1, where S _i = 2^t+1 - 2^t-i, i = O, 1,..., t - 1. Also they showed that the conjecture is true for i = O. In this paper we prove the correctness of this conjecture for Steiner trades.