  Protocol sequences are binary and periodic sequences used for deterministic
multiple access in a collision channel without feedback. In this paper, we
focus on user-irrepressible (UI) protocol sequences that can guarantee a
positive individual throughput per sequence period with probability one for a
slot-synchronous channel, regardless of the delay offsets among the users. As
the sequence period has a fundamental impact on the worst-case channel access
delay, a common objective of designing UI sequences is to make the sequence
period as short as possible. Consider a communication channel that is shared by
$M$ active users, and assume that each protocol sequence has a constant Hamming
weight $w$. To attain a better delay performance than previously known UI
sequences, this paper presents a CRTm construction of UI sequences with
$w=M+1$, which is a variation of the previously known CRT construction. For all
non-prime $M\geq 8$, our construction produces the shortest known sequence
period and the shortest known worst-case delay of UI sequences. Numerical
results show that the new construction enjoys a better average delay
performance than the optimal random access scheme and other constructions with
the same sequence period, in a variety of traffic conditions. In addition, we
derive an asymptotic lower bound on the minimum sequence period for $w=M+1$ if
the sequence structure satisfies some technical conditions, called
equi-difference, and prove the tightness of this lower bound by using the CRTm
construction.
