We study medium access control layer random access under the assumption that the receiver can perform successive interference cancellation, without feedback. During recent years, a number of protocols with impressive error performance have been suggested for this channel model. However, the random nature of these protocols causes an error floor which limits their usability when targeting ultra-reliable communications. In very recent works by Paolini et al. and Boyd et. al., it was shown that if each user employs predetermined combinatorial access patterns, this error floor disappears. In this paper, we develop code design criteria for deterministic random access protocols in the ultra-reliability region, and build codes based on these principles. The suggested design methods are supported by simulations.