THE LINEAR DISCREPANCY OF 3 × 3 × 3

$3{\times}3{\times}3$ is the meaningful smallest product of three chains of each size 2n+1 since $1{\times}1{\times}1$ is a 1-element poset. The linear discrepancy of the product of three chains $2n{\times}2n{\times}2n$ is found as $6n^3-2n^2-1$. But the case of the product of three chains $(2n + 1){\times}(2n + 1){\times}(2n + 1)$ is not known yet. In this paper, we determine ld$(3{\times}3{\times}3)$ as a case to determine the linear discrepancy of the product of three chains of each size 2n + 1.