Best Known (26−15, 26, s)-Nets in Base 256
(26−15, 26, 518)-Net over F256 — Constructive and digital
Digital (11, 26, 518)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (2, 17, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256 (see above)
- digital (2, 9, 259)-net over F256, using
(26−15, 26, 790)-Net over F256 — Digital
Digital (11, 26, 790)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25626, 790, F256, 15) (dual of [790, 764, 16]-code), using
- 14 step Varšamov–Edel lengthening with (ri) = (1, 13 times 0) [i] based on linear OA(25625, 775, F256, 15) (dual of [775, 750, 16]-code), using
- construction XX applied to C1 = C([251,264]), C2 = C([250,263]), C3 = C1 + C2 = C([251,263]), and C∩ = C1 ∩ C2 = C([250,264]) [i] based on
- linear OA(25623, 771, F256, 14) (dual of [771, 748, 15]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {251,252,…,264}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(25623, 771, F256, 14) (dual of [771, 748, 15]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {250,251,…,263}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(25625, 771, F256, 15) (dual of [771, 746, 16]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {250,251,…,264}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(25621, 771, F256, 13) (dual of [771, 750, 14]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {251,252,…,263}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([251,264]), C2 = C([250,263]), C3 = C1 + C2 = C([251,263]), and C∩ = C1 ∩ C2 = C([250,264]) [i] based on
- 14 step Varšamov–Edel lengthening with (ri) = (1, 13 times 0) [i] based on linear OA(25625, 775, F256, 15) (dual of [775, 750, 16]-code), using
(26−15, 26, 5287315)-Net in Base 256 — Upper bound on s
There is no (11, 26, 5287316)-net in base 256, because
- 1 times m-reduction [i] would yield (11, 25, 5287316)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 1 606938 799363 879966 630786 881518 845527 164631 419180 042256 629836 > 25625 [i]