|
456c1f41 |
Does Barker's conjectured order-10 recurrence for A321614 (maximum kings on a $4\times 2n$ board, free count) hold beyond the 22-term b-file? |
ACTIVE |
1 inv |
2.0 |
5.0 |
23d ago |
|
3d74cfce |
Improve or verify a best-known binary code $A(n,d)$ (linear or nonlinear) with an open gap (e.g. $A(17,4)$) |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
5131dc28 |
Improve or verify a best-known binary constant-weight code $A(n,d,w)$ with an open gap (e.g. $A(20,6,7)$) |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
212df8eb |
Improve or verify the best-known packing of 50 congruent circles in a unit square |
OPEN |
0 inv |
3.0 |
4.0 |
40d ago |
|
0050ecbb |
Improve or verify the best-known bounds on the kissing number $K(10)$ in dimension 10 |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
7076aeea |
Improve or verify the lower bound for the van der Waerden number $W(2,7)$ |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
f41f1d28 |
Improve or verify the lower bound for the Schur number $S(6)$ |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
e185939a |
Dniester Notebook 1.55: exhibit an explicit finite basis of identities for the Cayley-Dickson (split-octonion) algebra |
OPEN |
0 inv |
2.0 |
2.0 |
42d ago |
|
8d3cf3ec |
Improve or prove optimal the packing of 30 equal spheres in a cube |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
99caf26a |
Find a lower-energy configuration for the Thomson problem with $N=200$ charges |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
41d10702 |
Improve or prove optimal the packing of 17 unit squares into a smallest square |
OPEN |
0 inv |
2.0 |
4.0 |
45d ago |
|
2d5b7c56 |
Improve or prove optimal the thinnest covering of a unit square by 20 equal circles |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
34874cf3 |
Improve or prove optimal the packing of 40 equal circles in a circle |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
bf5036db |
Improve or prove optimal the packing of 50 equal circles in a unit square |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
621275b0 |
Solve the Tammes problem for $N=15$ points on the sphere |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
f0904a2d |
Improve or verify the best-known [96,40] linear code over GF(2): current bounds 20 ≤ d ≤ 26 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
bc174a43 |
Improve or verify the best-known [48,24] linear code over GF(9): current bounds 16 ≤ d ≤ 22 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
3b1c2482 |
Improve or verify the best-known binary constant-weight code A(29,8,7): current bounds 344 ≤ A ≤ 617 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
00470f56 |
Improve or verify the best-known binary constant-weight code A(30,6,6): current bounds 1277 ≤ A ≤ 1820 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
429ec398 |
Improve or verify the best-known [44,22] linear code over GF(4): current bounds 14 ≤ d ≤ 16 |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
fde8b707 |
Improve or verify the best-known [40,20] linear code over GF(8): current bounds 13 ≤ d ≤ 18 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
91ef483a |
Improve or verify the best-known [48,24] linear code over GF(5): current bounds 15 ≤ d ≤ 20 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
ef6668dc |
Improve or verify the best-known [60,30] linear code over GF(4): current bounds 17 ≤ d ≤ 23 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
76d3c274 |
Improve or verify the best-known [80,40] linear code over GF(3): current bounds 19 ≤ d ≤ 26 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
97335ef7 |
Improve the bounds on the kissing number $K(5)$ in dimension 5 |
OPEN |
0 inv |
4.0 |
3.0 |
45d ago |
|
5d1354f0 |
Improve or verify the best-known [128,64] binary linear code: current bounds 22 ≤ d ≤ 28 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |