Best Known (19, 19+27, s)-Nets in Base 256
(19, 19+27, 520)-Net over F256 — Constructive and digital
Digital (19, 46, 520)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (3, 16, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- digital (3, 30, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256 (see above)
- digital (3, 16, 260)-net over F256, using
(19, 19+27, 792)-Net over F256 — Digital
Digital (19, 46, 792)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25646, 792, F256, 27) (dual of [792, 746, 28]-code), using
- 16 step Varšamov–Edel lengthening with (ri) = (1, 15 times 0) [i] based on linear OA(25645, 775, F256, 27) (dual of [775, 730, 28]-code), using
- construction XX applied to C1 = C([245,270]), C2 = C([244,269]), C3 = C1 + C2 = C([245,269]), and C∩ = C1 ∩ C2 = C([244,270]) [i] based on
- linear OA(25643, 771, F256, 26) (dual of [771, 728, 27]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {245,246,…,270}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(25643, 771, F256, 26) (dual of [771, 728, 27]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {244,245,…,269}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(25645, 771, F256, 27) (dual of [771, 726, 28]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {244,245,…,270}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25641, 771, F256, 25) (dual of [771, 730, 26]-code), using the BCH-code C(I) with length 771 | 2562−1, defining interval I = {245,246,…,269}, and designed minimum distance d ≥ |I|+1 = 26 [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([245,270]), C2 = C([244,269]), C3 = C1 + C2 = C([245,269]), and C∩ = C1 ∩ C2 = C([244,270]) [i] based on
- 16 step Varšamov–Edel lengthening with (ri) = (1, 15 times 0) [i] based on linear OA(25645, 775, F256, 27) (dual of [775, 730, 28]-code), using
(19, 19+27, 4820373)-Net in Base 256 — Upper bound on s
There is no (19, 46, 4820374)-net in base 256, because
- 1 times m-reduction [i] would yield (19, 45, 4820374)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 2 348543 860511 098642 284127 704409 231313 338938 325872 969099 222239 219964 452228 852084 840220 911370 775285 302601 736686 > 25645 [i]