The paper presents an approach by which absolute error bounds may be derived for the continuous channel, thus determining the limits of the performance of a modulation and coding scheme. The code is considered as a set of points inn-dimensional space, and the concept of a sphere-packing inndimensions based on the regular simplex is used to determine the maximum packing density. The effect of code points on the edges of the signal space is also considered. Upper and lower bounds on the error rate are derived for various code rates and various block lengths (numbers of dimensions). The results are of relevance to combined coding/modulation schemes, andn-dimensional coding schemes, and show that a coding advantage of approximately 2dB is obtained for every doubling of the number of dimensions.