Best Known (15, 15+20, s)-Nets in Base 256
(15, 15+20, 519)-Net over F256 — Constructive and digital
Digital (15, 35, 519)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (3, 23, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (2, 12, 259)-net over F256, using
(15, 15+20, 864)-Net over F256 — Digital
Digital (15, 35, 864)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25635, 864, F256, 20) (dual of [864, 829, 21]-code), using
- 87 step Varšamov–Edel lengthening with (ri) = (1, 86 times 0) [i] based on linear OA(25634, 776, F256, 20) (dual of [776, 742, 21]-code), using
- construction XX applied to C1 = C([248,266]), C2 = C([247,264]), C3 = C1 + C2 = C([248,264]), and C∩ = C1 ∩ C2 = C([247,266]) [i] based on
- linear OA(25631, 771, F256, 19) (dual of [771, 740, 20]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {248,249,…,266}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25631, 771, F256, 18) (dual of [771, 740, 19]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {247,248,…,264}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(25633, 771, F256, 20) (dual of [771, 738, 21]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {247,248,…,266}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(25629, 771, F256, 17) (dual of [771, 742, 18]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {248,249,…,264}, and designed minimum distance d ≥ |I|+1 = 18 [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([248,266]), C2 = C([247,264]), C3 = C1 + C2 = C([248,264]), and C∩ = C1 ∩ C2 = C([247,266]) [i] based on
- 87 step Varšamov–Edel lengthening with (ri) = (1, 86 times 0) [i] based on linear OA(25634, 776, F256, 20) (dual of [776, 742, 21]-code), using
(15, 15+20, 4767334)-Net in Base 256 — Upper bound on s
There is no (15, 35, 4767335)-net in base 256, because
- the generalized Rao bound for nets shows that 256m ≥ 1 942672 599716 406608 977514 262007 592503 000157 908817 250280 802334 312443 625413 278906 909876 > 25635 [i]