Best Known (17, 17+23, s)-Nets in Base 256
(17, 17+23, 520)-Net over F256 — Constructive and digital
Digital (17, 40, 520)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 14, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (3, 26, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256 (see above)
- digital (3, 14, 260)-net over F256, using
(17, 17+23, 864)-Net over F256 — Digital
Digital (17, 40, 864)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25640, 864, F256, 23) (dual of [864, 824, 24]-code), using
- 87 step Varšamov–Edel lengthening with (ri) = (1, 86 times 0) [i] based on linear OA(25639, 776, F256, 23) (dual of [776, 737, 24]-code), using
- construction XX applied to C1 = C([118,139]), C2 = C([117,137]), C3 = C1 + C2 = C([118,137]), and C∩ = C1 ∩ C2 = C([117,139]) [i] based on
- linear OA(25636, 771, F256, 22) (dual of [771, 735, 23]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {118,119,…,139}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(25636, 771, F256, 21) (dual of [771, 735, 22]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {117,118,…,137}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25638, 771, F256, 23) (dual of [771, 733, 24]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {117,118,…,139}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25634, 771, F256, 20) (dual of [771, 737, 21]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {118,119,…,137}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, 256, F256, 1) (dual of [256, 255, 2]-code), using
- Reed–Solomon code RS(255,256) [i]
- discarding factors / shortening the dual code based on linear OA(2561, 256, F256, 1) (dual of [256, 255, 2]-code), using
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction XX applied to C1 = C([118,139]), C2 = C([117,137]), C3 = C1 + C2 = C([118,137]), and C∩ = C1 ∩ C2 = C([117,139]) [i] based on
- 87 step Varšamov–Edel lengthening with (ri) = (1, 86 times 0) [i] based on linear OA(25639, 776, F256, 23) (dual of [776, 737, 24]-code), using
(17, 17+23, 6649346)-Net in Base 256 — Upper bound on s
There is no (17, 40, 6649347)-net in base 256, because
- 1 times m-reduction [i] would yield (17, 39, 6649347)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 8343 703485 462201 249561 931123 756004 121208 480200 359397 597849 356931 189068 289076 833696 639876 814336 > 25639 [i]