Best Known (208−16, 208, s)-Nets in Base 2
(208−16, 208, 1048614)-Net over F2 — Constructive and digital
Digital (192, 208, 1048614)-net over F2, using
- 22 times duplication [i] based on digital (190, 206, 1048614)-net over F2, using
- t-expansion [i] based on digital (189, 206, 1048614)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (13, 21, 39)-net over F2, using
- digital (168, 185, 1048575)-net over F2, using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- t-expansion [i] based on digital (189, 206, 1048614)-net over F2, using
(208−16, 208, 1878230)-Net over F2 — Digital
Digital (192, 208, 1878230)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2208, 1878230, F2, 4, 16) (dual of [(1878230, 4), 7512712, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2208, 2097190, F2, 4, 16) (dual of [(2097190, 4), 8388552, 17]-NRT-code), using
- strength reduction [i] based on linear OOA(2208, 2097190, F2, 4, 17) (dual of [(2097190, 4), 8388552, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(221, 39, F2, 4, 8) (dual of [(39, 4), 135, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (13, 21, 39)-net over F2, using
- linear OOA(2187, 2097151, F2, 4, 17) (dual of [(2097151, 4), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2187, 4194302, F2, 2, 17) (dual of [(4194302, 2), 8388417, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2185, 4194301, F2, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 2-folding [i] based on linear OA(2185, 8388602, F2, 17) (dual of [8388602, 8388417, 18]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2185, 4194301, F2, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2187, 4194302, F2, 2, 17) (dual of [(4194302, 2), 8388417, 18]-NRT-code), using
- linear OOA(221, 39, F2, 4, 8) (dual of [(39, 4), 135, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- strength reduction [i] based on linear OOA(2208, 2097190, F2, 4, 17) (dual of [(2097190, 4), 8388552, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2208, 2097190, F2, 4, 16) (dual of [(2097190, 4), 8388552, 17]-NRT-code), using
(208−16, 208, large)-Net in Base 2 — Upper bound on s
There is no (192, 208, large)-net in base 2, because
- 14 times m-reduction [i] would yield (192, 194, large)-net in base 2, but