Multidimensional Costas Arrays and Their Enumeration Using GPUs and FPGAs

Table 1

Experimental results for MPCA enumerations.

𝑁		GPU		FPGA		Speedup
	MPCAs found^†	Time (secs)	Growth rate^⋆	Time (secs)	Growth rate	FPGA versus GPU
ℤ3^2	12	3.626	—	1.24e − 4	—	29241
ℤ5^2	80	20389	1.72	662	2.63	30.76
ℤ7^2	336^‡	1.87e14	3.15	7.42e14	3.18	25.21

^†MPCAs starting with (*; 0). As explained in Section 5, the rest of the MPCAs can be obtained using symmetries.
^⋆Growth rate is computed as:
(𝑝²_(𝑛+1)−𝑝²_(𝑛))^𝑇(ℤ_𝑝(𝑛+1))²/^𝑇(ℤ_𝑝(𝑛))².
^‡Lower bound of MPCAs based on Welch Costas construction and symmetries presented in [13].