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"path": "/blog/tech/2026-03-21-16-19_a286874_16_48.html",
"publishedAt": "2026-03-21T15:38:26.224Z",
"site": "http://blog.sesse.net",
"tags": [
"previous post"
],
"textContent": "Following up on the previous post, here are some heuristic results:\n\nFirst, if restricting oneself to 5-uniform values (all values have exactly five bits set), the best 15-bit code one can make is indeed 42 elements, and there are two distinct solutions: {31, 227, 364, 692, 1240, 1577, 1606, 2353, 3008, 3205, 3338, 4434, 4746, 4869, 5536, 6182, 6217, 7696, 8582, 8984, 9266, 9537, 10324, 10408, 10755, 12433, 12896, 13324, 16777, 16977, 17186, 17684, 18578, 18956, 19552, 20536, 20676, 21507, 24613, 24650, 26240, 30976} and {31, 227, 364, 692, 849, 906, 1240, 2354, 3206, 3337, 3680, 4485, 5169, 5442, 5644, 6228, 6312, 6659, 8745, 9285, 9632, 9746, 10314, 10385, 11012, 12326, 12568, 12992, 16966, 17450, 17684, 18049, 18469, 18880, 18968, 20553, 20626, 21280, 24688, 24716, 24835, 31744}. This supports, but does not prove, the conjecture that A286874(15) = 42.\n\nSecond, A286874(16) >= 48 (the best previously known bound was 45), since this is a valid 48-element solution:\n\n\n 0000000000011111\n 0000000011100011\n 0000000101101100\n 0000001010110100\n 0000010011011000\n 0000011100000011\n 0000100100110001\n 0000101000101010\n 0000101111000000\n 0001000110001001\n 0001010000110010\n 0001011000001100\n 0001100100000110\n 0001110001000001\n 0010000110010010\n 0010010010000101\n 0010011001100000\n 0010100001010100\n 0010110100001000\n 0011000001001010\n 0011001000010001\n 0011100010100000\n 0100001001001001\n 0100010001000110\n 0100010110100000\n 0100100010001100\n 0100111000010000\n 0101000000100101\n 0101000101010000\n 0101001010000010\n 0110000000111000\n 0110001100000100\n 0110100000000011\n 1000001001010010\n 1000010000101001\n 1000010100010100\n 1000101000000101\n 1000110010000010\n 1001000011000100\n 1001001100100000\n 1001100000011000\n 1010000000100110\n 1010000101000001\n 1010001010001000\n 1100000010010001\n 1100000100001010\n 1100100001100000\n 1111010000000000\n\n\nI won't be sweeping all of the 15- or 16-bit spaces.",
"title": "Steinar H. Gunderson: A286874(16) >= 48",
"updatedAt": "2026-03-21T15:19:00.000Z"
}