One or more storage media storing instructions which, when executed on a computer, cause the computer to perform a method of encoding video, the method comprising: selecting one of a plurality of scan orders; outputting information indicating the selected scan order in a bit stream; applying the selected scan order to reorder plural frequency coefficients of a block of a picture of the video; entropy coding the reordered plural frequency coefficients using a multi-level nested-set representation of the reordered plural frequency coefficients, including: representing a first set of one or more of the reordered plural frequency coefficients as a summary representation with a first symbol at a first level of the multi-level nested-set representation; entropy coding the first symbol and a second symbol at the first level of the multi-level nested-set representation; at a given level of the multi-level nested-set representation of the reordered plural frequency coefficients: encoding plural symbols at the given level, each of the plural symbols at the given level representing a set of one or more of the reordered plural frequency coefficients; and for each of the plural symbols at the given level, determining whether to split the set for the symbol into plural subsets and, if so, encoding plural symbols at a lower level of the multi-level nested-set representation of the reordered plural frequency coefficients, each of the plural symbols at the lower level representing one of the plural subsets; and outputting the entropy coded frequency coefficients in the bit stream. selecting one of a plurality of scan orders; outputting information indicating the selected scan order in a bit stream; applying the selected scan order to reorder plural frequency coefficients of a block of a picture of the video; entropy coding the reordered plural frequency coefficients using a multi-level nested-set representation of the reordered plural frequency coefficients, including: representing a first set of one or more of the reordered plural frequency coefficients as a summary representation with a first symbol at a first level of the multi-level nested-set representation; entropy coding the first symbol and a second symbol at the first level of the multi-level nested-set representation; at a given level of the multi-level nested-set representation of the reordered plural frequency coefficients: encoding plural symbols at the given level, each of the plural symbols at the given level representing a set of one or more of the reordered plural frequency coefficients; and for each of the plural symbols at the given level, determining whether to split the set for the symbol into plural subsets and, if so, encoding plural symbols at a lower level of the multi-level nested-set representation of the reordered plural frequency coefficients, each of the plural symbols at the lower level representing one of the plural subsets; and representing a first set of one or more of the reordered plural frequency coefficients as a summary representation with a first symbol at a first level of the multi-level nested-set representation; entropy coding the first symbol and a second symbol at the first level of the multi-level nested-set representation; at a given level of the multi-level nested-set representation of the reordered plural frequency coefficients: encoding plural symbols at the given level, each of the plural symbols at the given level representing a set of one or more of the reordered plural frequency coefficients; and for each of the plural symbols at the given level, determining whether to split the set for the symbol into plural subsets and, if so, encoding plural symbols at a lower level of the multi-level nested-set representation of the reordered plural frequency coefficients, each of the plural symbols at the lower level representing one of the plural subsets; and encoding plural symbols at the given level, each of the plural symbols at the given level representing a set of one or more of the reordered plural frequency coefficients; and for each of the plural symbols at the given level, determining whether to split the set for the symbol into plural subsets and, if so, encoding plural symbols at a lower level of the multi-level nested-set representation of the reordered plural frequency coefficients, each of the plural symbols at the lower level representing one of the plural subsets; and outputting the entropy coded frequency coefficients in the bit stream.