Spatially balanced sampling is an emerging area in statistical sampling. These designs are popular because they are one way to ensure the selected sample has spatial coverage over the entire survey area. This feature of spatial coverage aids in the resultant sample being representative of the population of interest. One of the first and the most commonly used spatially balanced design is called GRTS (Generalized Random Tessellation Stratified sampling) where sample effort is spread evenly over the target region. The term spread evenly in this context means having coverage of survey effort over the region. The coverage from GRTS has a stochastic component rather than a fixed interval, regularly spaced coverage as in a systematic sampling design. We have extended the idea of GRTS to a new design called Balances Acceptance Sampling (BAS). The BAS design allows surveys to be balanced in dimensions higher then two (n - dimensional space). Until now, most designs have considered balance in 2-D geographic space. With BAS we can achieve balance in 3-D space, or in higher dimensions. In some applications these dimensions can be features other than the spatial measures of geographic location, and the design allows aspects such as time for repeat surveys to be incorporated into sample balance.