Best Known (208, 225, s)-Nets in Base 2
(208, 225, 1048831)-Net over F2 — Constructive and digital
Digital (208, 225, 1048831)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (32, 40, 256)-net over F2, using
- net defined by OOA [i] based on linear OOA(240, 256, F2, 8, 8) (dual of [(256, 8), 2008, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(240, 1024, F2, 8) (dual of [1024, 984, 9]-code), using
- 1 times truncation [i] based on linear OA(241, 1025, F2, 9) (dual of [1025, 984, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 220−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(241, 1025, F2, 9) (dual of [1025, 984, 10]-code), using
- OA 4-folding and stacking [i] based on linear OA(240, 1024, F2, 8) (dual of [1024, 984, 9]-code), using
- net defined by OOA [i] based on linear OOA(240, 256, F2, 8, 8) (dual of [(256, 8), 2008, 9]-NRT-code), 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
- digital (32, 40, 256)-net over F2, using
(208, 225, 1850659)-Net over F2 — Digital
Digital (208, 225, 1850659)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2225, 1850659, F2, 4, 17) (dual of [(1850659, 4), 7402411, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2225, 2097406, F2, 4, 17) (dual of [(2097406, 4), 8389399, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2225, 4194812, F2, 2, 17) (dual of [(4194812, 2), 8389399, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2225, 4194813, F2, 2, 17) (dual of [(4194813, 2), 8389401, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(240, 512, F2, 2, 8) (dual of [(512, 2), 984, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(240, 1024, F2, 8) (dual of [1024, 984, 9]-code), using
- 1 times truncation [i] based on linear OA(241, 1025, F2, 9) (dual of [1025, 984, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 220−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(241, 1025, F2, 9) (dual of [1025, 984, 10]-code), using
- OOA 2-folding [i] based on linear OA(240, 1024, F2, 8) (dual of [1024, 984, 9]-code), using
- 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
- linear OOA(240, 512, F2, 2, 8) (dual of [(512, 2), 984, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2225, 4194813, F2, 2, 17) (dual of [(4194813, 2), 8389401, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2225, 4194812, F2, 2, 17) (dual of [(4194812, 2), 8389399, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2225, 2097406, F2, 4, 17) (dual of [(2097406, 4), 8389399, 18]-NRT-code), using
(208, 225, large)-Net in Base 2 — Upper bound on s
There is no (208, 225, large)-net in base 2, because
- 15 times m-reduction [i] would yield (208, 210, large)-net in base 2, but