Block-Wise Universal Bimagic and Semi-Bimagic Squares With Digits 1 and 8

In many papers, author worked with two digits such as, {1, 8}, {2, 5} and {6, 9}. Bimagic and semi-bimagic squares of order 8, 16, 24, 25 and 32 are studied previous works. This work brings bimagic and semi-bimagic squares of orders 48, 64 and 128 using only the digits 1 and 8. The order 64 is as multiples of blocks of orders 8 and 16, while the orders 48 and 128 are as multiples of orders 16. The previous results such as of orders 8, 16, 24 and 32 are also written again. The magic squares studied are upside-down and reflexive, i.e., universal magic squares.