Median selection networks with fewer comparators at small depth (49, 51, 56, 62, 63 and 64 inputs)

Median selection networks that use fewer comparators than any network with at most as many layers in Bert Dobbelaere's list of median selection networks (https://bertdobbelaere.github.io/median_networks.html, page generated 25 October 2026, read 26 October 2026): 49 inputs: 264 comparators, 19 layers (listed: 267 comparators with 19 layers, Mason Hemmer) 51 inputs: 281 comparators, 19 layers (listed: 283 comparators with 19 layers, Mason Hemmer) 56 inputs: 321 comparators, 18 layers (listed: 322 comparators with 18 layers, generated by the list (SorterHunter)) 62 inputs: 347 comparators, 19 layers (listed: 350 comparators with 19 layers, derived by the list from its 64-input network) 63 inputs: 354 comparators, 20 layers (listed: 356 comparators with 20 layers, Mason Hemmer) 64 inputs: 359 comparators, 19 layers (listed: 362 comparators with 19 layers, generated by the list (SorterHunter)) Each network is a new (size, depth) point that no listed network matches or beats on both counts. They were found by a local search that keeps the depth fixed, started from listed networks, and by the derivations described on the list page (removing inputs, adding a central comparator). verify.py (Python standard library) checks each network exactly through the 0-1 principle: it computes the exact set of states reachable after the first part of the network for the input weights at the median threshold and runs the rest of the network on all of them. A self-test compares the method with brute force on 201 small networks. Searches and verification were carried out with Claude (Anthropic) under the direction of Kerem Özdemir.